Geometries on surfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York
Cambridge University Press
2001
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
v. 84 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Description based on print version record |
| Beschreibung: | 1 online resource (xxii, 490 pages) illustrations |
| ISBN: | 0521660580 110708928X 9780511549656 9780521660587 9781107089280 |
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| 490 | 0 | |a Encyclopedia of mathematics and its applications |v v. 84 | |
| 500 | |a Description based on print version record | ||
| 505 | 8 | |a "The projective, Mobius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces that satisfy an axiom of joining. This book summarises all known major results and open problems related to these classical geometries and their close (non-classical) relatives." "Topics covered include: classical geometries; methods for constructing non-classical geometries; classifications and characterisations of geometries. This work is related to a host of other fields including interpolation theory, convexity, differential geometry, topology, the theory of Lie groups and many more. The authors detail these connections, some of which are well-known, but many much less so." "Acting both as a referee for experts and as an accessible introduction for beginners, this book will interest anyone wishing to know more about incidence geometries and the way they interact."--Jacket | |
| 505 | 8 | 0 | |t Geometries for Pedestrians -- |t Geometries of Points and Lines -- |t Geometries on Surfaces -- |t Flat Linear Spaces -- |t Models of the Classical Flat Projective Plane -- |t Convexity Theory -- |t Continuity of Geometric Operations and the Line Space -- |t Isomorphisms, Automorphism Groups, and Polarities -- |t Topological Planes and Flat Linear Spaces -- |t Classification with Respect to the Group Dimension -- |t Constructions -- |t Planes with Special Properties -- |t Other Invariants and Characterizations -- |t Related Geometries -- |t Spherical Circle Planes -- |t Models of the Classical Flat Mobius Plane -- |t Derived Planes and Topological Properties -- |t Constructions -- |t Groups of Automorphisms and Groups of Projectivities -- |t The Hering Types -- |t Characterizations of the Classical Plane -- |t Planes with Special Properties -- |t Subgeometries and Lie Geometries -- |t Toroidal Circle Planes -- |t Models of the Classical Flat Minkowski Plane -- |t Derived Planes and Topological Properties -- |t Constructions -- |t Automorphism Groups and Groups of Projectivities -- |t The Klein-Kroll Types -- |t Characterizations of the Classical Plane -- |t Planes with Special Properties -- |t Subgeometries and Lie Geometries -- |t Cylindrical Circle Planes -- |t Models of the Classical Flat Laguerre Plane -- |t Derived Planes and Topological Properties -- |t Constructions -- |t Automorphism Groups and Groups of Projectivities -- |t The Kleinewillinghofer Types -- |t Characterizations of the Classical Plane -- |t Planes with Special Properties -- |t Subgeometries and Lie Geometries -- |t Generalized Quadrangles |
| 650 | 4 | |a Géométrie projective | |
| 650 | 4 | |a Surfaces (Mathématiques) | |
| 650 | 7 | |a Topologie |2 gtt | |
| 650 | 7 | |a Inzidenzgeometrie |2 swd | |
| 650 | 7 | |a Topologische Geometrie |2 swd | |
| 650 | 7 | |a Geometry, Projective |2 fast | |
| 650 | 7 | |a Surfaces |2 fast | |
| 650 | 7 | |a MATHEMATICS / Geometry / General |2 bisacsh | |
| 650 | 4 | |a Geometry, Projective | |
| 650 | 4 | |a Surfaces | |
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Datensatz im Suchindex
| _version_ | 1804175393719058432 |
|---|---|
| any_adam_object | |
| author | Polster, Burkard |
| author_facet | Polster, Burkard |
| author_role | aut |
| author_sort | Polster, Burkard |
| author_variant | b p bp |
| building | Verbundindex |
| bvnumber | BV043034679 |
| collection | ZDB-4-EBA |
| contents | "The projective, Mobius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces that satisfy an axiom of joining. This book summarises all known major results and open problems related to these classical geometries and their close (non-classical) relatives." "Topics covered include: classical geometries; methods for constructing non-classical geometries; classifications and characterisations of geometries. This work is related to a host of other fields including interpolation theory, convexity, differential geometry, topology, the theory of Lie groups and many more. The authors detail these connections, some of which are well-known, but many much less so." "Acting both as a referee for experts and as an accessible introduction for beginners, this book will interest anyone wishing to know more about incidence geometries and the way they interact."--Jacket Geometries for Pedestrians -- Geometries of Points and Lines -- Geometries on Surfaces -- Flat Linear Spaces -- Models of the Classical Flat Projective Plane -- Convexity Theory -- Continuity of Geometric Operations and the Line Space -- Isomorphisms, Automorphism Groups, and Polarities -- Topological Planes and Flat Linear Spaces -- Classification with Respect to the Group Dimension -- Constructions -- Planes with Special Properties -- Other Invariants and Characterizations -- Related Geometries -- Spherical Circle Planes -- Models of the Classical Flat Mobius Plane -- Derived Planes and Topological Properties -- Groups of Automorphisms and Groups of Projectivities -- The Hering Types -- Characterizations of the Classical Plane -- Subgeometries and Lie Geometries -- Toroidal Circle Planes -- Models of the Classical Flat Minkowski Plane -- Automorphism Groups and Groups of Projectivities -- The Klein-Kroll Types -- Cylindrical Circle Planes -- Models of the Classical Flat Laguerre Plane -- The Kleinewillinghofer Types -- Generalized Quadrangles |
| ctrlnum | (OCoLC)861692510 (DE-599)BVBBV043034679 |
| dewey-full | 516/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.5 |
| dewey-search | 516/.5 |
| dewey-sort | 3516 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043034679 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:15:35Z |
| institution | BVB |
| isbn | 0521660580 110708928X 9780511549656 9780521660587 9781107089280 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028459329 |
| oclc_num | 861692510 |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 online resource (xxii, 490 pages) illustrations |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Polster, Burkard Verfasser aut Geometries on surfaces Burkard Polster and Günter Steinke Cambridge ; New York Cambridge University Press 2001 1 online resource (xxii, 490 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications v. 84 Description based on print version record "The projective, Mobius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces that satisfy an axiom of joining. This book summarises all known major results and open problems related to these classical geometries and their close (non-classical) relatives." "Topics covered include: classical geometries; methods for constructing non-classical geometries; classifications and characterisations of geometries. This work is related to a host of other fields including interpolation theory, convexity, differential geometry, topology, the theory of Lie groups and many more. The authors detail these connections, some of which are well-known, but many much less so." "Acting both as a referee for experts and as an accessible introduction for beginners, this book will interest anyone wishing to know more about incidence geometries and the way they interact."--Jacket Geometries for Pedestrians -- Geometries of Points and Lines -- Geometries on Surfaces -- Flat Linear Spaces -- Models of the Classical Flat Projective Plane -- Convexity Theory -- Continuity of Geometric Operations and the Line Space -- Isomorphisms, Automorphism Groups, and Polarities -- Topological Planes and Flat Linear Spaces -- Classification with Respect to the Group Dimension -- Constructions -- Planes with Special Properties -- Other Invariants and Characterizations -- Related Geometries -- Spherical Circle Planes -- Models of the Classical Flat Mobius Plane -- Derived Planes and Topological Properties -- Constructions -- Groups of Automorphisms and Groups of Projectivities -- The Hering Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Toroidal Circle Planes -- Models of the Classical Flat Minkowski Plane -- Derived Planes and Topological Properties -- Constructions -- Automorphism Groups and Groups of Projectivities -- The Klein-Kroll Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Cylindrical Circle Planes -- Models of the Classical Flat Laguerre Plane -- Derived Planes and Topological Properties -- Constructions -- Automorphism Groups and Groups of Projectivities -- The Kleinewillinghofer Types -- Characterizations of the Classical Plane -- Planes with Special Properties -- Subgeometries and Lie Geometries -- Generalized Quadrangles Géométrie projective Surfaces (Mathématiques) Topologie gtt Inzidenzgeometrie swd Topologische Geometrie swd Geometry, Projective fast Surfaces fast MATHEMATICS / Geometry / General bisacsh Geometry, Projective Surfaces Fläche (DE-588)4129864-0 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Fläche (DE-588)4129864-0 s Geometrie (DE-588)4020236-7 s 1\p DE-604 Steinke, Günter 1955- Sonstige oth Erscheint auch als Druck-Ausgabe Polster, Burkard Geometries on surfaces http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569250 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Polster, Burkard Geometries on surfaces "The projective, Mobius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces that satisfy an axiom of joining. This book summarises all known major results and open problems related to these classical geometries and their close (non-classical) relatives." "Topics covered include: classical geometries; methods for constructing non-classical geometries; classifications and characterisations of geometries. This work is related to a host of other fields including interpolation theory, convexity, differential geometry, topology, the theory of Lie groups and many more. The authors detail these connections, some of which are well-known, but many much less so." "Acting both as a referee for experts and as an accessible introduction for beginners, this book will interest anyone wishing to know more about incidence geometries and the way they interact."--Jacket Geometries for Pedestrians -- Geometries of Points and Lines -- Geometries on Surfaces -- Flat Linear Spaces -- Models of the Classical Flat Projective Plane -- Convexity Theory -- Continuity of Geometric Operations and the Line Space -- Isomorphisms, Automorphism Groups, and Polarities -- Topological Planes and Flat Linear Spaces -- Classification with Respect to the Group Dimension -- Constructions -- Planes with Special Properties -- Other Invariants and Characterizations -- Related Geometries -- Spherical Circle Planes -- Models of the Classical Flat Mobius Plane -- Derived Planes and Topological Properties -- Groups of Automorphisms and Groups of Projectivities -- The Hering Types -- Characterizations of the Classical Plane -- Subgeometries and Lie Geometries -- Toroidal Circle Planes -- Models of the Classical Flat Minkowski Plane -- Automorphism Groups and Groups of Projectivities -- The Klein-Kroll Types -- Cylindrical Circle Planes -- Models of the Classical Flat Laguerre Plane -- The Kleinewillinghofer Types -- Generalized Quadrangles Géométrie projective Surfaces (Mathématiques) Topologie gtt Inzidenzgeometrie swd Topologische Geometrie swd Geometry, Projective fast Surfaces fast MATHEMATICS / Geometry / General bisacsh Geometry, Projective Surfaces Fläche (DE-588)4129864-0 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4020236-7 |
| title | Geometries on surfaces |
| title_alt | Geometries for Pedestrians -- Geometries of Points and Lines -- Geometries on Surfaces -- Flat Linear Spaces -- Models of the Classical Flat Projective Plane -- Convexity Theory -- Continuity of Geometric Operations and the Line Space -- Isomorphisms, Automorphism Groups, and Polarities -- Topological Planes and Flat Linear Spaces -- Classification with Respect to the Group Dimension -- Constructions -- Planes with Special Properties -- Other Invariants and Characterizations -- Related Geometries -- Spherical Circle Planes -- Models of the Classical Flat Mobius Plane -- Derived Planes and Topological Properties -- Groups of Automorphisms and Groups of Projectivities -- The Hering Types -- Characterizations of the Classical Plane -- Subgeometries and Lie Geometries -- Toroidal Circle Planes -- Models of the Classical Flat Minkowski Plane -- Automorphism Groups and Groups of Projectivities -- The Klein-Kroll Types -- Cylindrical Circle Planes -- Models of the Classical Flat Laguerre Plane -- The Kleinewillinghofer Types -- Generalized Quadrangles |
| title_auth | Geometries on surfaces |
| title_exact_search | Geometries on surfaces |
| title_full | Geometries on surfaces Burkard Polster and Günter Steinke |
| title_fullStr | Geometries on surfaces Burkard Polster and Günter Steinke |
| title_full_unstemmed | Geometries on surfaces Burkard Polster and Günter Steinke |
| title_short | Geometries on surfaces |
| title_sort | geometries on surfaces |
| topic | Géométrie projective Surfaces (Mathématiques) Topologie gtt Inzidenzgeometrie swd Topologische Geometrie swd Geometry, Projective fast Surfaces fast MATHEMATICS / Geometry / General bisacsh Geometry, Projective Surfaces Fläche (DE-588)4129864-0 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Géométrie projective Surfaces (Mathématiques) Topologie Inzidenzgeometrie Topologische Geometrie Geometry, Projective Surfaces MATHEMATICS / Geometry / General Fläche Geometrie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569250 |
| work_keys_str_mv | AT polsterburkard geometriesonsurfaces AT steinkegunter geometriesonsurfaces |