
Aspects of Differential Geometry I
Morgan and Claypool Life Sciences (Publisher)
Published on 28. February 2015
Book
Paperback/Softback
154 pages
978-1-62705-662-5 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
San Rafael, CA
United States
Publishing group
Morgan & Claypool Publishers
Dimensions
Height: 235 mm
Width: 187 mm
Weight
333 gr
ISBN-13
978-1-62705-662-5 (9781627056625)
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Schweitzer Classification
Content
- Preface
- Acknowledgments
- Basic Notions and Concepts
- Manifolds
- Riemannian and Pseudo-Riemannian Geometry
- Bibliography
- Authors' Biographies
- Index
- Acknowledgments
- Basic Notions and Concepts
- Manifolds
- Riemannian and Pseudo-Riemannian Geometry
- Bibliography
- Authors' Biographies
- Index