Okubo T. Differential Geometry

Издательство Marcel Dekker, 1987, -816 pp.
I have written this book with the upper-level undergraduate and graduate students in mind. The purpose of the text is to provide a background for the study of local and global differential geometry. In particular, we are interested in tensor analysis developed on differentiable manifolds. The prerequisites are kept at a minimum, avoiding complete proofs of propositions and theorems that might require elaborate machinery. The material is arranged so as to proceed from the general to the special, and is accompanied in almost every section by exercises designed to enhance understanding of the definitions and theorems. Each topic is explained in a manner relating notation expressed in coordinates with coordinate-free expressions. This will help students explore the classical references and the abstractions currently adopted in most recent research papers.
Differentiable Manifolds.
Theory of Connections.
Riemannian Manifolds.
Theory of Submanifolds.
Complex Manifolds.
Homogeneous and Symmetric Spaces.
G-Structures and Transformation Groups.
Calculus of Variations for Lengths of Geodesics.
The de Rham Theorem, Characteristic Classes, and Harmonic Forms.