Differential Geometry of Manifolds

"Differential Geometry of Manifolds" discusses the theory of differentiable and Riemannian manifolds to help students understand the basic structures and consequent developments. Since the tangent vector plays a crucial role in the study of differentiable manifolds, this idea has been thoroughly discussed. In the theory of Riemannian geometry some new proofs have been included to enable the reader understand the subject in a comprehensive and systematic manner. This book will also benefit the postgraduate students as well as researchers working in the field of differential geometry and its applications to general relativity and cosmology. "The book...provides a profound introduction to the basic theory of differentiable and Riemannian manifolds. The author have tried to keep the treatment of the advanced material as lucid and comprehensive as possible - mainly by including utmost detailed calculations, numerous illustrating examples, and a wealth of complementing exercises with complete solutions - making the book easily accessible even to beginners in the field, the consistent use of the modern coordinate-free method of global differential geometry from the beginning on that characterizes the authors' utmost efficient didactical approach. The present textbook - one of the outstanding standard primers of modern differential geometry, and that as a basic source for a profound introductory course or as a highly recommendable reference for effective self-study of the subject likewise." (U.C. De, A.A. Shaikh Zentralblatt MATH 1143 - 1/2008).