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Geometry of Mb̲ius transformations : elliptic, parabolic and hyperbolic actions of SL2(R) /
This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surpr...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; London :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn860492548 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 120925s2012 si a ob 001 0 eng d | ||
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| 019 | |a 804661892 | ||
| 020 | |a 1848168594 | ||
| 020 | |a 9781848168596 | ||
| 029 | 1 | |a AU@ |b 000058199827 | |
| 029 | 1 | |a DEBBG |b BV044167541 | |
| 029 | 1 | |a DEBSZ |b 379329433 | |
| 029 | 1 | |a DEBSZ |b 45499768X | |
| 035 | |a (OCoLC)860492548 |z (OCoLC)804661892 | ||
| 050 | 4 | |a QA171 | |
| 082 | 0 | 4 | |a 516.1 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Kisil, Vladimir V. | |
| 245 | 1 | 0 | |a Geometry of Mb̲ius transformations : |b elliptic, parabolic and hyperbolic actions of SL2(R) / |c by Vladimir V. Kisil. |
| 260 | |a Singapore ; |a London : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (xiv, 192 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 500 | |a 1 DVD-ROM in plastic pocket inside front cover. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; List of Figures; 1. Erlangen Programme: Preview; 1.1 Make a Guess in Three Attempts; 1.2 Covariance of FSCc; 1.3 Invariants: Algebraic and Geometric; 1.4 Joint Invariants: Orthogonality; 1.5 Higher-order Joint Invariants: Focal Orthogonality; 1.6 Distance, Length and Perpendicularity; 1.7 The Erlangen Programme at Large; 2. Groups and Homogeneous Spaces; 2.1 Groups and Transformations; 2.2 Subgroups and Homogeneous Spaces; 2.2.1 From a Homogeneous Space to the Isotropy Subgroup; 2.2.2 From a Subgroup to the Homogeneous Space. | |
| 505 | 8 | |a 2.3 Differentiation on Lie Groups and Lie Algebras2.3.1 One-parameter Subgroups and Lie Algebras; 2.3.2 Invariant Vector Fields and Lie Algebras; 2.3.3 Commutator in Lie Algebras; 3. Homogeneous Spaces from the Group SL2(R); 3.1 The Affine Group and the Real Line; 3.2 One-dimensional Subgroups of SL2(R); 3.3 Two-dimensional Homogeneous Spaces; 3.3.1 From the Subgroup K; 3.3.2 From the Subgroup N; 3.3.3 From the Subgroup A; 3.3.4 Unifying All Three Cases; 3.4 Elliptic, Parabolic and Hyperbolic Cases; 3.5 Orbits of the Subgroup Actions; 3.6 Unifying EPH Cases: The First Attempt. | |
| 505 | 8 | |a 3.7 Isotropy Subgroups4. The Extended Fillmore-Springer-Cnops Construction; 4.1 Invariance of Cycles; 4.2 Projective Spaces of Cycles; 4.3 Covariance of FSCc; 4.4 Origins of FSCc; 4.4.1 Projective Coordiantes and Polynomials; 4.4.2 Co-Adjoint Representation; 4.5 Projective Cross-Ratio; 5. Indefinite Product Space of Cycles; 5.1 Cycles: An Appearance and the Essence; 5.2 Cycles as Vectors; 5.3 Invariant Cycle Product; 5.4 Zero-radius Cycles; 5.5 Cauchy-Schwarz Inequality and Tangent Cycles; 6. Joint Invariants of Cycles: Orthogonality; 6.1 Orthogonality of Cycles; 6.2 Orthogonality Miscellanea. | |
| 505 | 8 | |a 6.3 Ghost Cycles and Orthogonality6.4 Actions of FSCc Matrices; 6.5 Inversions and Reflections in Cycles; 6.6 Higher-order Joint Invariants: Focal Orthogonality; 7. Metric Invariants in Upper Half-Planes; 7.1 Distances; 7.2 Lengths; 7.3 Conformal Properties of Mobius Maps; 7.4 Perpendicularity and Orthogonality; 7.5 Infinitesimal-radius Cycles; 7.6 Infinitesimal Conformality; 8. Global Geometry of Upper Half-Planes; 8.1 Compactification of the Point Space; 8.2 (Non)-Invariance of The Upper Half-Plane; 8.3 Optics and Mechanics; 8.3.1 Optics; 8.3.2 Classical Mechanics; 8.3.3 Quantum Mechanics. | |
| 505 | 8 | |a 8.4 Relativity of Space-Time9. Invariant Metric and Geodesics; 9.1 Metrics, Curves' Lengths and Extrema; 9.2 Invariant Metric; 9.3 Geodesics: Additivity of Metric; 9.4 Geometric Invariants; 9.5 Invariant Metric and Cross-Ratio; 10. Conformal Unit Disk; 10.1 Elliptic Cayley Transforms; 10.2 Hyperbolic Cayley Transform; 10.3 Parabolic Cayley Transforms; 10.4 Cayley Transforms of Cycles; 10.4.1 Cayley Transform and FSSc; 10.4.2 Geodesics on the Disks; 11. Unitary Rotations; 11.1 Unitary Rotations -An Algebraic Approach; 11.2 Unitary Rotations -A Geometrical Viewpoint. | |
| 520 | |a This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). 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 Möbius transformations is provide. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Mb̲ius transformations. | |
| 650 | 0 | |a Transformations (Mathematics) | |
| 650 | 7 | |a Transformations (Mathematics) |2 fast | |
| 776 | 0 | |c Hardback |z 9781848168589 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=982518 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL982518 | ||
| 994 | |a 92 |b IZTAP | ||