Bieberbach Groups and Flat Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1986
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced material. To satisfy this reference persona, I'll begin by telling you a little about the subject matter of the book, and then I'll talk about the textbook aspect. A flat riemannian manifold is a space in which you can talk about geometry (e. g. distance, angle, curvature, "straight lines," etc. ) and, in addition, the geometry is locally the one we all know and love, namely euclidean geometry. This means that near any point of this space one can introduce coordinates so that with respect to these coordinates, the rules of euclidean geometry hold. These coordinates are not valid in the entire space, so you can't conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "flat manifold" to mean "compact flat riemannian manifold. " It turns out that the most important invariant for flat manifolds is the fundamental group |
| Beschreibung: | 1 Online-Ressource (XIII, 242p) |
| ISBN: | 9781461386872 9780387963952 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4613-8687-2 |
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Datensatz im Suchindex
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| author | Charlap, Leonard S. |
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| author_sort | Charlap, Leonard S. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-8687-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
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| isbn | 9781461386872 9780387963952 |
| issn | 0172-5939 |
| language | English |
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| spelling | Charlap, Leonard S. Verfasser aut Bieberbach Groups and Flat Manifolds by Leonard S. Charlap New York, NY Springer New York 1986 1 Online-Ressource (XIII, 242p) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Many mathematics books suffer from schizophrenia, and this is yet another. On the one hand it tries to be a reference for the basic results on flat riemannian manifolds. On the other hand it attempts to be a textbook which can be used for a second year graduate course. My aim was to keep the second personality dominant, but the reference persona kept breaking out especially at the end of sections in the form of remarks that contain more advanced material. To satisfy this reference persona, I'll begin by telling you a little about the subject matter of the book, and then I'll talk about the textbook aspect. A flat riemannian manifold is a space in which you can talk about geometry (e. g. distance, angle, curvature, "straight lines," etc. ) and, in addition, the geometry is locally the one we all know and love, namely euclidean geometry. This means that near any point of this space one can introduce coordinates so that with respect to these coordinates, the rules of euclidean geometry hold. These coordinates are not valid in the entire space, so you can't conclude the space is euclidean space itself. In this book we are mainly concerned with compact flat riemannian manifolds, and unless we say otherwise, we use the term "flat manifold" to mean "compact flat riemannian manifold. " It turns out that the most important invariant for flat manifolds is the fundamental group Mathematics Group theory Cell aggregation / Mathematics Group Theory and Generalizations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Flache Mannigfaltigkeit (DE-588)4300461-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Bieberbach-Gruppe (DE-588)4128293-0 gnd rswk-swf Automorphe Funktion (DE-588)4143706-8 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s Bieberbach-Gruppe (DE-588)4128293-0 s 1\p DE-604 Riemannscher Raum (DE-588)4128295-4 s 2\p DE-604 Flache Mannigfaltigkeit (DE-588)4300461-1 s 3\p DE-604 Automorphe Funktion (DE-588)4143706-8 s 4\p DE-604 Gruppentheorie (DE-588)4072157-7 s 5\p DE-604 https://doi.org/10.1007/978-1-4613-8687-2 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 | Charlap, Leonard S. Bieberbach Groups and Flat Manifolds Mathematics Group theory Cell aggregation / Mathematics Group Theory and Generalizations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Flache Mannigfaltigkeit (DE-588)4300461-1 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Bieberbach-Gruppe (DE-588)4128293-0 gnd Automorphe Funktion (DE-588)4143706-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4300461-1 (DE-588)4049991-1 (DE-588)4128293-0 (DE-588)4143706-8 (DE-588)4128295-4 (DE-588)4072157-7 |
| title | Bieberbach Groups and Flat Manifolds |
| title_auth | Bieberbach Groups and Flat Manifolds |
| title_exact_search | Bieberbach Groups and Flat Manifolds |
| title_full | Bieberbach Groups and Flat Manifolds by Leonard S. Charlap |
| title_fullStr | Bieberbach Groups and Flat Manifolds by Leonard S. Charlap |
| title_full_unstemmed | Bieberbach Groups and Flat Manifolds by Leonard S. Charlap |
| title_short | Bieberbach Groups and Flat Manifolds |
| title_sort | bieberbach groups and flat manifolds |
| topic | Mathematics Group theory Cell aggregation / Mathematics Group Theory and Generalizations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Flache Mannigfaltigkeit (DE-588)4300461-1 gnd Riemannsche Fläche (DE-588)4049991-1 gnd Bieberbach-Gruppe (DE-588)4128293-0 gnd Automorphe Funktion (DE-588)4143706-8 gnd Riemannscher Raum (DE-588)4128295-4 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Mathematics Group theory Cell aggregation / Mathematics Group Theory and Generalizations Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Flache Mannigfaltigkeit Riemannsche Fläche Bieberbach-Gruppe Automorphe Funktion Riemannscher Raum Gruppentheorie |
| url | https://doi.org/10.1007/978-1-4613-8687-2 |
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