By Serge Lang

ISBN-10: 0387943382

ISBN-13: 9780387943381

ISBN-10: 1461286883

ISBN-13: 9781461286882

this can be the 3rd model of a booklet on differential manifolds. the 1st model seemed in 1962, and was once written on the very starting of a interval of serious enlargement of the topic. on the time, i discovered no passable ebook for the principles of the topic, for a number of purposes. I increased the publication in 1971, and that i extend it nonetheless additional at the present time. in particular, i've got additional 3 chapters on Riemannian and pseudo Riemannian geometry, that's, covariant derivatives, curvature, and a few functions as much as the Hopf-Rinow and Hadamard-Cartan theorems, in addition to a few calculus of diversifications and functions to quantity varieties. i've got rewritten the sections on sprays, and i've given extra examples of using Stokes' theorem. i've got additionally given many extra references to the literature, all of this to expand the viewpoint of the publication, which i am hoping can be utilized between issues for a normal path best into many instructions. the current ebook nonetheless meets the outdated wishes, yet fulfills new ones. on the most elementary point, the ebook supplies an creation to the fundamental innovations that are utilized in differential topology, differential geometry, and differential equations. In differential topology, one reports for example homotopy periods of maps and the potential for discovering appropriate differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

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Differential and Riemannian Manifolds (Graduate Texts in Mathematics) by Serge Lang


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