| 000 -LEADER |
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| fixed length control field |
05267nam a2200709 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
8694982 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20200413152932.0 |
| 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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| fixed length control field |
cr bn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
190503s2019 caua fob 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781681735641 |
| Qualifying information |
electronic |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781681735658 |
| Qualifying information |
hardcover |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781681735634 |
| Qualifying information |
paperback |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.2200/S00917ED1V04Y201904MAS026 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(CaBNVSL)thg00978847 |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)1099982222 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
CaBNVSL |
| Language of cataloging |
eng |
| Description conventions |
rda |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA641 |
| Item number |
.C252 2019eb |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
516.36 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Calviño-Louzao, Esteban, |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Aspects of differential geometry IV / |
| Statement of responsibility, etc. |
Esteban Calviño-Louzao, Eduardo García-Río, Peter Gilkey, JeongHyeong Park, Ramón Vázquez-Lorenzo. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
[San Rafael, California] : |
| Name of producer, publisher, distributor, manufacturer |
Morgan & Claypool, |
| Date of production, publication, distribution, manufacture, or copyright notice |
[2019] |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 PDF (xvii, 149 pages) : |
| Other physical details |
illustrations (some color). |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
electronic |
| Source |
isbdmedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
#26 |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
System requirements: Adobe Acrobat Reader. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (pages 137-141) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
12. An introduction to affine geometry -- 12.1. Basic definitions -- 12.2. Surfaces with recurrent Ricci tensor -- 12.3. The affine quasi-Einstein equation -- 12.4. The classification of locally homogeneous affine surfaces with torsion -- 12.5. Analytic structure for homogeneous affine surfaces |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
13. The geometry of type A models -- 13.1. Type A : foundational results and basic examples -- 13.2. Type A : distinguished geometries -- 13.3. Type A : parameterization -- 13.4. Type A : moduli spaces |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
14. The geometry of type B models -- 14.1. Type B : distinguished geometries -- 14.2. Type B : affine killing vector fields -- 14.3. Symmetric spaces |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
15. Applications of affine surface theory -- 15.1. Preliminary matters -- 15.2. Signature (2, 2) VSI manifolds -- 15.3. Signature (2, 2) bach flat manifolds. |
| 506 ## - 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 |
|---|
| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces which are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group R2 is Abelian and the ax + b group is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type A surfaces. These are the left-invariant affine geometries on R2. Associating to each Type A surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue [mu] = -1 turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type B surfaces; these are the left-invariant affine geometries on the ax + b group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere S2. The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
|---|
| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Title from PDF title page (viewed on May 3, 2019). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Geometry, Differential. |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
affine gradient Ricci solitons |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
affine Killing vector fields |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
geodesic completeness |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
locally homogeneous affine surfaces |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
locally symmetric affine surfaces |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
projectively flat |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
quasi-Einstein equation |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
García-Río, Eduardo, |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Gilkey, Peter B., |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Park, Jeonghyeong, |
| Relator term |
author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Vázquez-Lorenzo, Ramón, |
| Relator term |
author |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| International Standard Book Number |
9781681735658 |
| -- |
9781681735634 |
| 830 #0 - SERIES 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 ; |
| Volume/sequential designation |
#26. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to full text |
| Uniform Resource Identifier |
https://doi.org/10.2200/S00917ED1V04Y201904MAS026 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
https://ieeexplore.ieee.org/servlet/opac?bknumber=8694982 |
