## Differential and Riemannian Manifolds (Graduate Texts in by Serge Lang

By Serge Lang

this can be the 3rd model of a booklet on differential manifolds. the 1st model seemed in 1962, and used to be written on the very starting of a interval of serious enlargement of the topic. on the time, i discovered no passable e-book for the rules of the topic, for a number of purposes. I multiplied the e-book in 1971, and that i extend it nonetheless extra 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 purposes 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 develop the point of view of the booklet, which i am hoping can be utilized between issues for a normal direction top into many instructions. the current booklet nonetheless meets the outdated wishes, yet fulfills new ones. on the most simple point, the publication provides an creation to the elemental recommendations that are utilized in differential topology, differential geometry, and differential equations. In differential topology, one experiences for example homotopy periods of maps and the opportunity of discovering appropriate differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

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