Geometry of möbius transformations: elliptic, parabolic and hyperbolic actions of SL2, (R)
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London, UK
Imperial College Press
2012
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and index Erlangen programme : preview -- Groups and homogeneous spaces -- Homogeneous spaces from the group SL₂(R) -- The extended Fillmore-Springer-Cnops construction -- Indefinite product space of cycles -- Joint invariants of cycles: orthogonality -- Metric invariants in upper half-planes -- Global geometry of upper half-planes -- Invariant metric and geodesics -- Conformal unit disk -- Unitary rotations This book is a unique exposition of rich and inspiring geometries associated with Mobius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL[symbol](real number). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F. Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered |
| Beschreibung: | 1 Online-Ressource (xiv, 192 pages) |
| ISBN: | 1848168594 9781848168596 |
Internformat
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| 245 | 1 | 0 | |a Geometry of möbius transformations |b elliptic, parabolic and hyperbolic actions of SL2, (R) |c Vladimir V. Kisil |
| 264 | 1 | |a London, UK |b Imperial College Press |c 2012 | |
| 300 | |a 1 Online-Ressource (xiv, 192 pages) | ||
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| 500 | |a Includes bibliographical references and index | ||
| 500 | |a Erlangen programme : preview -- Groups and homogeneous spaces -- Homogeneous spaces from the group SL₂(R) -- The extended Fillmore-Springer-Cnops construction -- Indefinite product space of cycles -- Joint invariants of cycles: orthogonality -- Metric invariants in upper half-planes -- Global geometry of upper half-planes -- Invariant metric and geodesics -- Conformal unit disk -- Unitary rotations | ||
| 500 | |a This book is a unique exposition of rich and inspiring geometries associated with Mobius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL[symbol](real number). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F. Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered | ||
| 650 | 7 | |a MATHEMATICS / Geometry / General |2 bisacsh | |
| 650 | 7 | |a Möbius transformations |2 fast | |
| 650 | 4 | |a Möbius transformations | |
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| 689 | 0 | 0 | |a Möbius-Geometrie |0 (DE-588)4750877-2 |D s |
| 689 | 0 | 1 | |a Kleinsche Gruppe |0 (DE-588)4164159-0 |D s |
| 689 | 0 | 2 | |a Transformation |0 (DE-588)4451062-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804175614510366720 |
|---|---|
| any_adam_object | |
| author | Kisil, Vladimir V. |
| author_facet | Kisil, Vladimir V. |
| author_role | aut |
| author_sort | Kisil, Vladimir V. |
| author_variant | v v k vv vvk |
| building | Verbundindex |
| bvnumber | BV043152742 |
| classification_rvk | SK 350 SK 750 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)801193203 (DE-599)BVBBV043152742 |
| dewey-full | 516.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.1 |
| dewey-search | 516.1 |
| dewey-sort | 3516.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043152742 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:05Z |
| institution | BVB |
| isbn | 1848168594 9781848168596 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028576933 |
| oclc_num | 801193203 |
| open_access_boolean | |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xiv, 192 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Kisil, Vladimir V. Verfasser aut Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) Vladimir V. Kisil London, UK Imperial College Press 2012 1 Online-Ressource (xiv, 192 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and index Erlangen programme : preview -- Groups and homogeneous spaces -- Homogeneous spaces from the group SL₂(R) -- The extended Fillmore-Springer-Cnops construction -- Indefinite product space of cycles -- Joint invariants of cycles: orthogonality -- Metric invariants in upper half-planes -- Global geometry of upper half-planes -- Invariant metric and geodesics -- Conformal unit disk -- Unitary rotations This book is a unique exposition of rich and inspiring geometries associated with Mobius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL[symbol](real number). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F. Klein, who defined geometry as a study of invariants under a transitive group action. The treatment of elliptic, parabolic and hyperbolic Mobius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered MATHEMATICS / Geometry / General bisacsh Möbius transformations fast Möbius transformations Möbius-Geometrie (DE-588)4750877-2 gnd rswk-swf Transformation (DE-588)4451062-7 gnd rswk-swf Kleinsche Gruppe (DE-588)4164159-0 gnd rswk-swf Möbius-Geometrie (DE-588)4750877-2 s Kleinsche Gruppe (DE-588)4164159-0 s Transformation (DE-588)4451062-7 s 1\p DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 1-84816-858-6 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-84816-858-9 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=479894 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kisil, Vladimir V. Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) MATHEMATICS / Geometry / General bisacsh Möbius transformations fast Möbius transformations Möbius-Geometrie (DE-588)4750877-2 gnd Transformation (DE-588)4451062-7 gnd Kleinsche Gruppe (DE-588)4164159-0 gnd |
| subject_GND | (DE-588)4750877-2 (DE-588)4451062-7 (DE-588)4164159-0 |
| title | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) |
| title_auth | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) |
| title_exact_search | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) |
| title_full | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) Vladimir V. Kisil |
| title_fullStr | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) Vladimir V. Kisil |
| title_full_unstemmed | Geometry of möbius transformations elliptic, parabolic and hyperbolic actions of SL2, (R) Vladimir V. Kisil |
| title_short | Geometry of möbius transformations |
| title_sort | geometry of mobius transformations elliptic parabolic and hyperbolic actions of sl2 r |
| title_sub | elliptic, parabolic and hyperbolic actions of SL2, (R) |
| topic | MATHEMATICS / Geometry / General bisacsh Möbius transformations fast Möbius transformations Möbius-Geometrie (DE-588)4750877-2 gnd Transformation (DE-588)4451062-7 gnd Kleinsche Gruppe (DE-588)4164159-0 gnd |
| topic_facet | MATHEMATICS / Geometry / General Möbius transformations Möbius-Geometrie Transformation Kleinsche Gruppe |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=479894 |
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