Aspects of differential geometry I /

Bibliographic Details
Main Authors:	Gilkey, Peter B. (Author), Park, Jeonghyeong (Author), Vázquez-Lorenzo, Ramón (Author)
Format:	eBook
Language:	English
Published:	San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool, 2015.
Series:	Synthesis lectures on mathematics and statistics ; # 15.
Subjects:	Geometry, Differential. Change of Variable Theorem Fubini's Theorem Gauss's Theorem Gauss-Bonnet Theorem Green's Theorem Implicit Function Theorem Inverse Function Theorem Levi-Civita connection Riemann integral Riemannian geometry Stokes' Theorem derivative as best linear approximation geodesic improper integrals partitions of unity pseudo-Riemannian geometry Electronic books.
Online Access:	Connect to the full text of this electronic book

Description
Abstract:	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.
Physical Description:	1 online resource (xiii, 140 pages) : illustrations. Also available in print.
Format:	Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader.
Bibliography:	Includes bibliographical references (pages 131-133) and index.
ISBN:	9781627056632
ISSN:	1938-1751 ;
DOI:	10.2200/S00632ED1V01Y201502MAS015
Access:	Abstract freely available; full-text restricted to subscribers or individual document purchasers.