Geometries on surfaces:
The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2001
|
| Series: | Encyclopedia of mathematics and its applications
volume 84 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, 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 reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xxii, 490 pages) |
| ISBN: | 9780511549656 |
| DOI: | 10.1017/CBO9780511549656 |
Staff View
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| 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 |
| 520 | |a The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, 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 reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact | ||
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Record in the Search Index
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| 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 | BV043942223 |
| classification_rvk | SK 370 SK 380 |
| collection | ZDB-20-CBO |
| contents | 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 | (ZDB-20-CBO)CR9780511549656 (OCoLC)849898462 (DE-599)BVBBV043942223 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511549656 |
| format | Electronic eBook |
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| id | DE-604.BV043942223 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511549656 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351192 |
| oclc_num | 849898462 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xxii, 490 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| 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 Cambridge University Press 2001 1 online resource (xxii, 490 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 84 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, 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 reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact 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 Druckausgabe 978-0-521-66058-7 https://doi.org/10.1017/CBO9780511549656 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Polster, Burkard Geometries on surfaces 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 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 | Geometry, Projective Surfaces Fläche (DE-588)4129864-0 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry, Projective Surfaces Fläche Geometrie |
| url | https://doi.org/10.1017/CBO9780511549656 |
| work_keys_str_mv | AT polsterburkard geometriesonsurfaces AT steinkegunter geometriesonsurfaces |