Riemannian Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry. Also, we present a -soft- proof of the Paul Levy-Gromov isoperimetric inequality, kindly communicated by G. Besson. Several people helped us to find bugs in the first edition. They are not responsible for the persisting ones! Among them, we particularly thank Pierre Arnoux and Stefano Marchiafava. We are also indebted to Marc Troyanov for valuable comments and suggestions. INTRODUCTION This book is an outgrowth of graduate lectures given by two of us in Paris. We assume that the reader has already heard a little about differential manifolds. At some very precise points, we also use the basic vocabulary of representation theory, or some elementary notions about homotopy. Now and then, some remarks and comments use more elaborate theories. Such passages are inserted between *. In most textbooks about Riemannian geometry, the starting point is the local theory of embedded surfaces. Here we begin directly with the so-called "abstract" manifolds. To illustrate our point of view, a series of examples is developed each time a new definition or theorem occurs. Thus, the reader will meet a detailed recurrent study of spheres, tori, real and complex projective spaces, and compact Lie groups equipped with bi-invariant metrics. Notice that all these examples, although very common, are not so easy to realize (except the first) as Riemannian submanifolds of Euclidean spaces |
| Beschreibung: | 1 Online-Ressource (XIII, 286 p) |
| ISBN: | 9783642972423 9783540524014 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-97242-3 |
Internformat
MARC
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| 245 | 1 | 0 | |a Riemannian Geometry |c by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| 250 | |a Second Edition | ||
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| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| author | Gallot, Sylvestre |
| author_facet | Gallot, Sylvestre |
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| author_variant | s g sg |
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| ctrlnum | (OCoLC)1165449850 (DE-599)BVBBV042423157 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-97242-3 |
| edition | Second Edition |
| format | Electronic eBook |
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| id | DE-604.BV042423157 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642972423 9783540524014 |
| issn | 0172-5939 |
| language | English |
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| spelling | Gallot, Sylvestre Verfasser aut Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine Second Edition Berlin, Heidelberg Springer Berlin Heidelberg 1990 1 Online-Ressource (XIII, 286 p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry. Also, we present a -soft- proof of the Paul Levy-Gromov isoperimetric inequality, kindly communicated by G. Besson. Several people helped us to find bugs in the first edition. They are not responsible for the persisting ones! Among them, we particularly thank Pierre Arnoux and Stefano Marchiafava. We are also indebted to Marc Troyanov for valuable comments and suggestions. INTRODUCTION This book is an outgrowth of graduate lectures given by two of us in Paris. We assume that the reader has already heard a little about differential manifolds. At some very precise points, we also use the basic vocabulary of representation theory, or some elementary notions about homotopy. Now and then, some remarks and comments use more elaborate theories. Such passages are inserted between *. In most textbooks about Riemannian geometry, the starting point is the local theory of embedded surfaces. Here we begin directly with the so-called "abstract" manifolds. To illustrate our point of view, a series of examples is developed each time a new definition or theorem occurs. Thus, the reader will meet a detailed recurrent study of spheres, tori, real and complex projective spaces, and compact Lie groups equipped with bi-invariant metrics. Notice that all these examples, although very common, are not so easy to realize (except the first) as Riemannian submanifolds of Euclidean spaces Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Riemannsche Geometrie (DE-588)4128462-8 gnd rswk-swf Riemannsche Geometrie (DE-588)4128462-8 s 1\p DE-604 Hulin, Dominique Sonstige oth Lafontaine, Jacques Sonstige oth https://doi.org/10.1007/978-3-642-97242-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gallot, Sylvestre Riemannian Geometry Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Riemannsche Geometrie (DE-588)4128462-8 gnd |
| subject_GND | (DE-588)4128462-8 |
| title | Riemannian Geometry |
| title_auth | Riemannian Geometry |
| title_exact_search | Riemannian Geometry |
| title_full | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_fullStr | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_full_unstemmed | Riemannian Geometry by Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine |
| title_short | Riemannian Geometry |
| title_sort | riemannian geometry |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Riemannsche Geometrie (DE-588)4128462-8 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Riemannsche Geometrie |
| url | https://doi.org/10.1007/978-3-642-97242-3 |
| work_keys_str_mv | AT gallotsylvestre riemanniangeometry AT hulindominique riemanniangeometry AT lafontainejacques riemanniangeometry |