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09596nam a2201105 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
6813736 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20200413152854.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
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m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
090604s2009 cau foab 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781598298208 (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| Canceled/invalid ISBN |
9781598298192 (pbk.) |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.2200/S00197ED1V01Y200906MAS005 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(CaBNVSL)gtp00534712 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)426825841 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
CaBNVSL |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA613 |
| Item number |
.G468 2009 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
516.07 |
| Edition number |
22 |
| 245 04 - TITLE STATEMENT |
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| Title |
The geometry of Walker manifolds |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
Miguel Brozos-Vázquez ... [et al]. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
|---|
| Place of publication, distribution, etc. |
San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : |
| Name of publisher, distributor, etc. |
Morgan & Claypool Publishers, |
| Date of publication, distribution, etc. |
c2009. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 electronic text (xvii, 159 p.) : |
| Other physical details |
digital file. |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1930-1751 ; |
| Volume/sequential designation |
# 5 |
| 538 ## - SYSTEM DETAILS NOTE |
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| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
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| System details note |
System requirements: Adobe Acrobat reader. |
| 500 ## - GENERAL NOTE |
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| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 500 ## - GENERAL NOTE |
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| General note |
Series from website. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes bibliographical references (p. 129-147) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Basic algebraic notions -- Introduction -- A historical perspective in the algebraic context -- Algebraic preliminaries -- Jordan normal form -- Indefinite geometry -- Algebraic curvature tensors -- Hermitian and para-Hermitian geometry -- The Jacobi and skew symmetric curvature operators -- Sectional, Ricci, scalar, and Weyl curvature -- Curvature decompositions -- Self-duality and anti-self-duality conditions -- Spectral geometry of the curvature operator -- Osserman and conformally Osserman models -- Osserman curvature models in signature (2, 2) -- Ivanov-Petrova curvature models -- Osserman Ivanov-Petrova curvature models -- Commuting curvature models -- Basic geometrical notions -- Introduction -- History -- Basic manifold theory -- The tangent bundle, lie bracket, and lie groups -- The cotangent bundle and symplectic geometry -- Connections, curvature, geodesics, and holonomy -- Pseudo-Riemannian geometry -- The Levi-Civita connection -- Associated natural operators -- Weyl scalar invariants -- Null distributions -- Pseudo-Riemannian holonomy -- Other geometric structures -- Pseudo-Hermitian and para-Hermitian structures -- Hyper-para-Hermitian structures -- Geometric realizations -- Homogeneous spaces, and curvature homogeneity -- Technical results in differential equations -- Walker structures -- Introduction -- Historical development -- Walker coordinates -- Examples of Walker manifolds -- Hypersurfaces with nilpotent shape operators -- Locally conformally flat metrics with nilpotent Ricci operator -- Degenerate pseudo-Riemannian homogeneous structures -- Para-Kaehler geometry -- Two-step nilpotent lie groups with degenerate center -- Conformally symmetric pseudo-Riemannian metrics -- Riemannian extensions -- The affine category -- Twisted Riemannian extensions defined by flat connections -- Modified Riemannian extensions defined by flat connections -- Nilpotent Walker manifolds -- Osserman Riemannian extensions -- Ivanov-Petrova Riemannian extensions -- Three-dimensional Lorentzian Walker manifolds -- Introduction -- History -- Three dimensional Walker geometry -- Adapted coordinates -- The Jordan normal form of the Ricci operator -- Christoffel symbols, curvature, and the Ricci tensor -- Locally symmetric Walker manifolds -- Einstein-like manifolds -- The spectral geometry of the curvature tensor -- Curvature commutativity properties -- Local geometry of Walker manifolds with -- Foliated Walker manifolds -- Contact Walker manifolds -- Strict Walker manifolds -- Three dimensional homogeneous Lorentzian manifolds -- Three dimensional lie groups and lie algebras -- Curvature homogeneous Lorentzian manifolds -- Diagonalizable Ricci operator -- Type II Ricci operator -- Four-dimensional Walker manifolds -- Introduction -- History -- Four-dimensional Walker manifolds -- Almost para-Hermitian geometry -- Isotropic almost para-Hermitian structures -- Characteristic classes -- Self-dual Walker manifolds -- The spectral geometry of the curvature tensor -- Introduction -- History -- Four-dimensional Osserman metrics -- Osserman metrics with diagonalizable Jacobi operator -- Osserman Walker type II metrics -- Osserman and Ivanov-Petrova metrics -- Riemannian extensions of affine surfaces -- Affine surfaces with skew symmetric Ricci tensor -- Affine surfaces with symmetric and degenerate Ricci tensor -- Riemannian extensions with commuting curvature operators -- Other examples with commuting curvature operators -- Hermitian geometry -- Introduction -- History -- Almost Hermitian geometry of Walker manifolds -- The proper almost Hermitian structure of a Walker manifold -- Proper almost hyper-para-Hermitian structures -- Hermitian Walker manifolds of dimension four -- Proper Hermitian Walker structures -- Locally conformally Kaehler structures -- Almost Kaehler Walker four-dimensional manifolds -- Special Walker manifolds -- Introduction -- History -- Curvature commuting conditions -- Curvature homogeneous strict Walker manifolds -- Bibliography. |
| 506 1# - RESTRICTIONS ON ACCESS NOTE |
|---|
| Terms governing access |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Compendex |
| 510 0# - CITATION/REFERENCES NOTE |
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| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
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| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo- Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible,we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
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| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
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| Source of description note |
Title from PDF t.p. (viewed on June 4, 2009). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Manifolds (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Riemannian manifolds. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Curvature. |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Affine connection |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Affine surface |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Almost Hermitian |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Almost Kaehler |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Christoffel symbols |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Codazzi Ricci tensor |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Commuting curvature model |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Conformally flat |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Conformally Kaehler |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Conformally Osserman |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Contact Walker manifold |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Curvature commuting |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Cyclic parallel Ricci tensor |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Einstein |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Flat connection |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Foliated Walker manifold |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Gray identity |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Geometry of the curvature operator |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Homogeneous space |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Hyper Hermitian |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Hyper-Kaehler |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Ivanov-Petrova |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Jacobi operator |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Levi-Civita connection |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Locally symmetric |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Lorentzian |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Nijenhuis tensor |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Nilpotent Walker manifold |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Null distribution |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Osserman curvature model |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Para-Hermitian |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Para-Kaehler |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Parallel null distribution |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Projectively flat |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Ricci anti-symmetric |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Ricci curvature |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Ricci flat |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Scalar curvature |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Riemannian extension |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Torsion free connection |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Schouten tensor |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Sectional curvature |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Skew-symetric curvature operator |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
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| Topical term or geographic name as entry element |
Tricerri-Vanhecke decomposition |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Vaisman manifold |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Vanishing scalar invariants |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Walker coordinates |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Walker manifold |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Weyl curvature |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) |
|---|
| Topical term or geographic name as entry element |
Weyl scalar invariants |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Brozos-Vázquez, Miguel. |
| 730 0# - ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis digital library of engineering and computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1930-1751 ; |
| Volume/sequential designation |
# 5. |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
http://ieeexplore.ieee.org/servlet/opac?bknumber=6813736 |
