Riemannian Manifolds An Introduction to Curvature /

• Main Author: Lee, John M. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 1997.
• Series: Graduate Texts in Mathematics, 176
• Subjects: Mathematics.; Differential geometry.; Differential Geometry.

This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introd...

Table of Contents:

• What Is Curvature?
• Review of Tensors, Manifolds, and Vector Bundles
• Definitions and Examples of Riemannian Metrics
• Connections
• Riemannian Geodesics
• Geodesics and Distance
• Curvature
• Riemannian Submanifolds
• The Gauss-Bonnet Theorem
• Jacobi Fields
• Curvature and Topology.