Introduction to Differential Geometry

Author: Shen Yibing
Publisher:
Publish Date: 2005-10-01
Features: This book originally compiled the author's insights and experiences in studying integral differential geometry and exterior calculus methods. It was published in 1998 by Hangzhou University Press and was intended as a textbook for senior undergraduate mathematics majors as an elective course. After its publication, it was highly valued and beloved by a wide readership and quickly went out of print. Many contents of the book were derived from the academic works and lectures of the renowned geometry master, Chen Shengshen. In 2001, when Mr. Chen visited Hangzhou, he praised the book highly and suggested adding more content and translating it into English. However, due to the author's procrastination, this promise was never fulfilled. Unexpectedly, Mr. Chen passed away suddenly on December 3, 2004. While mourning his loss, the author also deeply regretted this unfulfilled promise. The author wishes to dedicate this reprinted book to Mr. Chen! The main difference between this edition and the first edition is the addition of Chapter 5: Hypersurfaces in Higher-Dimensional Euclidean Spaces. This is the most direct and natural extension of the theory of surfaces in three-dimensional Euclidean space, and it is still developing. The book covers topics such as: the method of moving frames, the integral differential geometry of curves, the intrinsic geometry of surfaces, and hypersurfaces in higher-dimensional Euclidean spaces.