Differential manifolds and Riemannian manifolds

Author: S. LangLang
Publisher:
Publication Date: 1998-03-01
Features: This is the third version of a book on differential manifolds. The first version appeared in 1962 and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject for multiple reasons. I expanded the book in 1971, and I expand it even further today. Specifically, I have added three chapters on Riemannian and pseudo-Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten these sections on sprays and have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs but fulfills new ones.