Riemannian Geometry and Geometric Analysis (English Edition) (3rd Edition)

Author: None
Publisher:
Publish Date: 2005-06-01
Features: This book is a valuable graduate-level textbook, primarily focusing on the study of fundamental theorems in Riemannian geometry, such as the Hodge theorem, Rauch comparison theorem, and the existence of harmonic maps as proven by Lyusternik and Fet. It also includes hot topics in contemporary mathematical research, with some content appearing in textbooks for the first time. Each chapter is accompanied by exercises. Contents: Basic Theory; De Rham Cohomology and Harmonic Differential Forms; Parallel Transport, Connection, and Covariant Derivative; Geodesics and Jacobi Fields; Symmetric Spaces and K?hler Manifolds; Morse Theory and Floer Homology; Variational Problems in Quantum Field Theory; Harmonic Maps. Target Audience: Graduate students, teachers, and researchers in mathematics and theoretical physics.