Fundamentals of Differential Geometry

Serge Lang

ISBN 10: 1461268109 / ISBN 13: 9781461268109

Editore: Springer US, Springer New York, 2012

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9781461268109

Dati bibliografici

• Titolo: Fundamentals of Differential Geometry
• Editore: Springer US, Springer New York
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461268109
• ISBN 13: 9781461268109
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 31 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 31 millimetri di profondità
• Peso: 844 grammi

Descrizione articolo

Riassunto

This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. Although the book grew out of the author's earlier book "Differential and Riemannian Manifolds", the focus has now changed from the general theory of manifolds to general differential geometry.

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