Minimal differential geometry

Author: Ma Li
Publisher:
Publish Date: 2004-01-01
Features: Assuming readers have no prior knowledge of topology, this book introduces the main content of differential geometry. It primarily explains the theory of curves and surfaces in space, two-dimensional Riemannian manifolds, differentiable manifolds, differential forms, Lie derivatives, tensor theory, covariant derivatives, and curvature tensors. The book aims to combine classical and modern differential geometry for science and engineering students. Many examples are provided to help students understand the meaning of geometric concepts! The book also includes some new content, such as geodesics on ellipsoids, the derivation of the KdV equation, and the minimality of minimal surfaces in graphs, in order to emphasize the relationship between classical content and contemporary hot mathematical problems. Additionally, a certain number of exercises are arranged for readers to practice. This book is suitable for undergraduate and graduate students in science and engineering, as well as scholars interested in mathematics.