Fundamentals of Differential Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Graduate Texts in Mathematics
191 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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 |
| Beschreibung: | 1 Online-Ressource (XVII, 540 p) |
| ISBN: | 9781461205418 9781461268109 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-0541-8 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Lang, Serge |
| author_facet | Lang, Serge |
| author_role | aut |
| author_sort | Lang, Serge |
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| bvnumber | BV042419549 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 9781461205418 9781461268109 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (XVII, 540 p) |
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| spelling | Lang, Serge Verfasser aut Fundamentals of Differential Geometry by Serge Lang New York, NY Springer New York 1999 1 Online-Ressource (XVII, 540 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 191 0072-5285 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 Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 2\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 3\p DE-604 Differentialtopologie (DE-588)4012255-4 s 4\p DE-604 Spektraltheorie (DE-588)4116561-5 s 5\p DE-604 https://doi.org/10.1007/978-1-4612-0541-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lang, Serge Fundamentals of Differential Geometry Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Differentialtopologie (DE-588)4012255-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4012255-4 (DE-588)4012269-4 (DE-588)4116561-5 (DE-588)4151278-9 |
| title | Fundamentals of Differential Geometry |
| title_auth | Fundamentals of Differential Geometry |
| title_exact_search | Fundamentals of Differential Geometry |
| title_full | Fundamentals of Differential Geometry by Serge Lang |
| title_fullStr | Fundamentals of Differential Geometry by Serge Lang |
| title_full_unstemmed | Fundamentals of Differential Geometry by Serge Lang |
| title_short | Fundamentals of Differential Geometry |
| title_sort | fundamentals of differential geometry |
| topic | Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Differentialtopologie (DE-588)4012255-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialgeometrie Differentialtopologie Differenzierbare Mannigfaltigkeit Spektraltheorie Einführung |
| url | https://doi.org/10.1007/978-1-4612-0541-8 |
| work_keys_str_mv | AT langserge fundamentalsofdifferentialgeometry |