Introduction to Riemannian Geometry (Volume 1)

Author: Chen Weihuan
Publisher:
Publish Date: 2004-01-01
Features: "Introduction to Riemannian Geometry" is a foundational course for graduate students in basic mathematics. Since Riemann first introduced the concept of Riemannian geometry in 1954, the field has evolved from local theories to global theories. Today, Riemannian geometry has become a fundamental theory widely used in various branches of mathematics and physics. The first part of this book serves as the textbook for the "Introduction to Riemannian Geometry" course. The first four chapters cover the basics of Riemannian geometry; Chapters 5 and 6 introduce the variational methods of Riemannian geometry, providing an introduction to global Riemannian geometry; Chapter 7 explores the theory of submanifolds in Riemannian geometry. Each chapter ends with a large number of exercises, and the book includes answers and hints to the exercises at the end, facilitating in-depth learning and self-study. This book is suitable as a textbook for students and graduate researchers in mathematics and physics departments of comprehensive universities and normal universities, as well as for mathematicians to engage with.