EAN: 9783031012792

Bilder-Quelle: discount24.de - Sport-Freizeit

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. Table of Contents: Preface Acknowledgments Basic Notions and Concepts Manifolds Riemannian and Pseudo-Riemannian Geometry Bibliography Authors' Biographies Index

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