| 书目名称 | Differential and Riemannian Manifolds | | 编辑 | Serge Lang | | 视频video | | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | 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 still 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 the sections on sprays, and I 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. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one stud | | 出版日期 | Textbook 1995Latest edition | | 关键词 | De Rham cohomology; Hodge decomposition; Riemannian geometry; cohomology; curvature; differential geometr | | 版次 | 3 | | doi | https://doi.org/10.1007/978-1-4612-4182-9 | | isbn_softcover | 978-1-4612-8688-2 | | isbn_ebook | 978-1-4612-4182-9Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer-Verlag New York, Inc. 1995 |
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发表于 2025-3-21 19:11:25
