Aspects of differential geometry I /
By: Gilkey, Peter B [author.].
Contributor(s): Park, JeongHyeong [author.] | Vázquez-Lorenzo, Ramón [author.].
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mathematics and statistics: # 15.Publisher: San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2015.Description: 1 PDF (xiii, 140 pages) : illustrations.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781627056632.Subject(s): Geometry, Differential | Change of Variable Theorem | derivative as best linear approximation | Fubini's Theorem | Gauss-Bonnet Theorem | Gauss's Theorem | geodesic | Green's Theorem | Implicit Function Theorem | improper integrals | Inverse Function Theorem | Levi-Civita connection | partitions of unity | pseudo-Riemannian geometry | Riemann integral | Riemannian geometry | Stokes' TheoremDDC classification: 516.36 Online resources: Abstract with links to resource Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE622 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes bibliographical references (pages 131-133) and index.
1. Basic notions and concepts -- 1.1 Metric spaces -- 1.2 Linear algebra -- 1.3 The derivative -- 1.4 The inverse and implicit function theorems -- 1.5 The Riemann integral -- 1.6 Improper integrals -- 1.7 The change of variable theorem --
2. Manifolds -- 2.1 Smooth manifolds -- 2.2 The tangent and cotangent bundles -- 2.3 Stokes' theorem -- 2.4 Applications of stokes' theorem --
3. Riemannian and pseudo-Riemannian geometry -- 3.1 The pseudo-Riemannian measure -- 3.2 Connections -- 3.3 The Levi-Civita connection -- 3.4 Geodesics -- 3.5 The Jacobi operator -- 3.6 The Gauss-Bonnet theorem -- 3.7 The Chern-Gauss-Bonnet theorem --
Bibliography -- Authors' biographies -- Index.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
Compendex
INSPEC
Google scholar
Google book search
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.
Also available in print.
Title from PDF title page (viewed on March 20, 2015).
There are no comments for this item.