Preliminary Course in Differential Geometry

Author: Chen Weihuan
Publisher:
Publish Date: 1999-12-01
Features: This book is the textbook for the differential geometry course at the Department of Mathematics, Peking University. It primarily focuses on the local theory of curves and surfaces in three-dimensional Euclidean space, covering the following content: prerequisites, curve theory, the fundamental forms of surfaces, the second fundamental form of surfaces, the fundamental theorem of surface theory, geodesic curvature and geodesics, moving frames and exterior calculus. An appendix is included, which discusses the theorems of differential equations used in this book and introduces the concept of tensors. The book strives to align with the language and methods of modern differential geometry, therefore, it integrates modern manifold concepts as much as possible in the exposition and consistently uses frame fields attached to curves and surfaces. It provides a detailed introduction to exterior differential forms. The book is written in an accessible and clear manner, with rigorous arguments and a strong emphasis on geometric ideas, making it easy for readers to understand and master. This book can be used as a textbook for differential geometry courses in comprehensive universities and normal universities, as well as a teaching reference for self-study in higher education.