Differential Geometry Lectures

Author: Chen Shengshen, Chen Weiguan
Publisher:
Publish Date: 2001-10-01
Features: This book systematically discusses the fundamental knowledge of differential geometry. It consists of eight chapters and two appendices. The authors dedicate significant, particularly in Chapters 3 and 6, to introducing basic concepts and tools such as manifolds, multilinear functions, vector fields, exterior differentiation, Lie groups, and the method of moving frames. After establishing this broad and solid foundation, the book explores the core issues of differential geometry, including connections, Riemannian geometry, and surface theory. Chapter 7 on complex manifolds is both a highly active research area and one of the fields where the authors have made outstanding contributions, featuring their unique insights and concise methods. Chapter 8 on Finsler geometry, added in the second edition, is a research topic recently promoted by the authors. In this field, Chern connections exhibit prominent properties, making Riemannian geometry a special case of Finsler geometry. The last two appendices introduce global curve theory and surface theory, as well as discussions on the relationship between differential geometry and theoretical physics, proposing numerous further research topics in these two active frontiers. This book can serve as a textbook for senior undergraduate and graduate students in mathematics and theoretical physics, or as a reference book for self-study. It is also suitable for researchers in mathematics and physics and related disciplines.