Introduction to Differential Manifolds

Author: Chen Weihuan
Publisher:
Publish Date: 2004-04-01
Features: "A Graduate Textbook: An Introduction to Differentiable Manifolds" can be used as a textbook for graduate students and senior undergraduate students in mathematics departments of comprehensive universities, higher normal universities, for courses such as "Differentiable Manifolds," "Introduction to Riemannian Geometry," or "Modern Differential Geometry." It can also serve as a reference for students, teachers, and researchers in related fields such as mechanics and theoretical physics. "A Graduate Textbook: An Introduction to Differentiable Manifolds" is an introductory textbook on the theory of differentiable manifolds, serving as a bridge between classical mathematics and contemporary mathematical literature. Its main content includes introducing the basic concepts and examples of differentiable manifolds, smooth vector fields on differentiable manifolds, smooth tensor fields, the operations and properties of differential forms, as well as preliminary knowledge of Riemannian manifolds, Lie groups, and differential fiber bundles. The book is written in a clear, concise, and accessible manner, with a strong emphasis on geometric background, focusing on how to handle globally defined mathematical objects on differentiable manifolds using local coordinates. By studying "A Graduate Textbook: An Introduction to Differentiable Manifolds," readers will lay a solid foundation in the theory and applications of differentiable manifolds and create conditions for studying contemporary mathematical literature.