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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Fundamentals of Differential Geometry
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Fundamentals of Differential Geometry
Serge Lang (Gebundene Ausgabe, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.10.2001
Sprache
Englisch
EAN
9780387985930
Herausgeber
Springer US
Serien- oder Bandtitel
Graduate Texts in Mathematics
Sonderedition
Nein
Autor
Serge Lang
Seitenanzahl
540
Einbandart
Gebundene Ausgabe
Schlagwörter
Derivative, Riemannian geometry, Smooth function, calculus, curvature, differential equation, differential geometry, manifold, spectral theorem, vector bundle
Thema-Inhalt
PBPD - Algebraische Topologie
PBK - Mathematische Analysis, allgemein
Höhe
235 mm
Breite
15.5 cm
Hersteller: Humana, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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