Riemannian Geometry: An Introduction (Revised Edition)

Author: Bai Zhengguo et al.
Publisher:
Publish Date: 2004-12-01
Features: This book is an introductory textbook on Riemannian geometry, covering topics such as an introduction to differentiable manifolds, tensor analysis, the fundamentals of Riemannian geometry, geodesic theory, and submanifold geometry. The book provides a unified treatment of the three representations of Riemannian geometry—tensorial invariants, moving frames, and natural coordinates. It introduces various fundamental concepts and techniques in differentiable manifolds and Riemannian geometry, balancing classical theories with modern advancements to enable readers to conduct independent research after completing the course. The revised edition also includes six additional appendices to meet further reader requirements. This book can serve as a textbook for senior elective courses in mathematics departments of comprehensive universities, normal universities, and as a graduate-level textbook. It is also a valuable reference for mathematicians and physicists.