Fundamentals of Differential Geometry

Serge Lang

ISBN 10: 038798593X / ISBN 13: 9780387985930

Editore: Springer New York, Springer US Dez 1998, 1998

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Neuware -The present book aims to give a fairly comprehensive account of the fundamentals of differential manifolds and differential geometry. The size of the book influenced where to stop, and there would be enough material for a second volume (this is not a threat). 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 studies for instance homotopy classes of maps and the possibility of finding suitable differen tiable maps in them (immersions, embeddings, isomorphisms, etc. ). One may also use differentiable structures on topological manifolds to deter mine the topological structure of the manifold (for example, it la Smale [Sm 67]). In differential geometry, one puts an additional structure on the differentiable manifold (a vector field, a spray, a 2-form, a Riemannian metric, ad lib. ) and studies properties connected especially with these objects. Formally, one may say that one studies properties invariant under the group of differentiable automorphisms which preserve the additional structure. In differential equations, one studies vector fields and their in tegral curves, singular points, stable and unstable manifolds, etc. A certain number of concepts are essential for all three, and are so basic and elementary that it is worthwhile to collect them together so that more advanced expositions can be given without having to start from the very beginnings.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 564 pp. Englisch. Codice articolo 9780387985930

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Titolo: Fundamentals of Differential Geometry

Casa editrice: Springer New York, Springer US Dez 1998

Data di pubblicazione: 1998

Legatura: Buch

Condizione: Neu

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Riassunto:

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises.

From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

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