Differential and Riemannian Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1995
|
| Schriftenreihe: | Graduate Texts in Mathematics
160 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. 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 differentiable maps in them (immersions, embeddings, isomorphisms, etc.) |
| Beschreibung: | 1 Online-Ressource (XIV, 364 p) |
| ISBN: | 9781461241829 9781461286882 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4182-9 |
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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 |
| author_variant | s l sl |
| building | Verbundindex |
| bvnumber | BV042420238 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863757698 (DE-599)BVBBV042420238 |
| dewey-full | 515 |
| 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 |
| doi_str_mv | 10.1007/978-1-4612-4182-9 |
| format | Electronic eBook |
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| id | DE-604.BV042420238 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461241829 9781461286882 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855655 |
| oclc_num | 863757698 |
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| physical | 1 Online-Ressource (XIV, 364 p) |
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| publishDate | 1995 |
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| spelling | Lang, Serge Verfasser aut Differential and Riemannian Manifolds edited by Serge Lang New York, NY Springer New York 1995 1 Online-Ressource (XIV, 364 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 160 0072-5285 This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. 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 differentiable maps in them (immersions, embeddings, isomorphisms, etc.) Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 s 1\p DE-604 Riemannscher Raum (DE-588)4128295-4 s 2\p DE-604 Differentialtopologie (DE-588)4012255-4 s 3\p DE-604 Differentialgeometrie (DE-588)4012248-7 s 4\p DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 5\p DE-604 https://doi.org/10.1007/978-1-4612-4182-9 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 Differential and Riemannian Manifolds Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialtopologie (DE-588)4012255-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)4012269-4 (DE-588)4012248-7 (DE-588)4037379-4 (DE-588)4128295-4 |
| title | Differential and Riemannian Manifolds |
| title_auth | Differential and Riemannian Manifolds |
| title_exact_search | Differential and Riemannian Manifolds |
| title_full | Differential and Riemannian Manifolds edited by Serge Lang |
| title_fullStr | Differential and Riemannian Manifolds edited by Serge Lang |
| title_full_unstemmed | Differential and Riemannian Manifolds edited by Serge Lang |
| title_short | Differential and Riemannian Manifolds |
| title_sort | differential and riemannian manifolds |
| topic | Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialtopologie (DE-588)4012255-4 gnd Differenzierbare Mannigfaltigkeit (DE-588)4012269-4 gnd Differentialgeometrie (DE-588)4012248-7 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Algebraic topology Analysis Algebraic Topology Mathematik Differentialtopologie Differenzierbare Mannigfaltigkeit Differentialgeometrie Mannigfaltigkeit Riemannscher Raum |
| url | https://doi.org/10.1007/978-1-4612-4182-9 |
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