By Serge Lang (auth.), Serge Lang (eds.)
This is the 3rd model of a ebook on differential manifolds. the 1st model seemed in 1962, and used to be written on the very starting of a interval of serious growth of the topic. on the time, i discovered no passable e-book for the principles of the topic, for a number of purposes. I elevated the publication in 1971, and that i extend it nonetheless extra this present day. in particular, i've got extra 3 chapters on Riemannian and pseudo Riemannian geometry, that's, covariant derivatives, curvature, and a few purposes as much as the Hopf-Rinow and Hadamard-Cartan theorems, in addition to a few calculus of diversifications and functions to quantity types. 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'm hoping can be utilized between issues for a normal direction major into many instructions. the current publication nonetheless meets the previous wishes, yet fulfills new ones. on the most elementary point, the e-book provides an creation to the elemental options that are utilized in differential topology, differential geometry, and differential equations. In differential topology, one reports for example homotopy sessions of maps and the opportunity of discovering appropriate differentiable maps in them (immersions, embeddings, isomorphisms, etc.).
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