Author : Peter Gilkey
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1627056637
Total Pages : 156 pages
Book Rating : 4.6/5 (27 download)
Book Synopsis Aspects of Differential Geometry I by : Peter Gilkey
Download or read book Aspects of Differential Geometry I written by Peter Gilkey and published by Morgan & Claypool Publishers. This book was released on 2015-02-01 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.