Riemannian Geometry Selected Topics

Author: Wu Hongxi
Publisher:
Publish Date: 2000-02-01
Features: This book primarily discusses five important topics in the study of large-scale Riemannian geometry. The content includes: Hodge theory, harmonic groups, the structure of non-compact non-negative curvature manifolds, the Gauss-Bonnet theorem, and the convergence of Riemannian manifolds, among others. This book reflects the overall picture of large-scale Riemannian geometry research, with some content being presented systematically in lecture form for the first time. For example, it provides a complete elementary proof of the Hodge theorem; comprehensively summarizes the past and present of the theory of harmonic groups and their applications in contemporary geometric research; analyzes the intrinsic proof of the Gauss-Bonnet theorem by East; and introduces Gromov's theory of the convergence of Riemannian manifolds, guiding readers into the new frontiers of large-scale Riemannian geometry. The book is well-structured, rigorous in reasoning, and inspiring. It also pays special attention to introducing the historical background, fundamental ideas, and intrinsic connections between the various topics. This book can serve as a textbook for senior undergraduate and graduate students in mathematics departments of comprehensive universities and normal universities, as well as an important reference book for mathematicians to understand large-scale Riemannian geometry.