| GENERAL |
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Full Poncelet Theorem in Minkowski dS and AdS Spaces |
| WANG Yao-Xiong1, FAN Heng2, SHI Kang-Jie1, WANG Chun1, ZHANG Kai1, ZENG Yu1 |
| 1Institute of Modern Physics, Northwest University, Xi'an 7100692Institute of Physics, Chinese Academy of Sciences, Beijing 100190 |
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| Cite this article: |
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WANG Yao-Xiong, FAN Heng, SHI Kang-Jie et al 2009 Chin. Phys. Lett. 26 010201 |
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Abstract We study the reflection of a straight line or a billiard on a plane in an n-dimensional Minkowski space. It is found that the reflection law coincides with that defined with respect to confocal quadratic surfaces in projective geometry. We then establish the full Poncelet theorem which holds in projective geometry in n-dimensional Minkowski space and in their quadratic surfaces including de Sitter and AdS spaces.
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| Keywords:
02.40.Dr
02.30.Ik
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Received: 08 October 2008
Published: 24 December 2008
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| PACS: |
02.40.Dr
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(Euclidean and projective geometries)
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02.30.Ik
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(Integrable systems)
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[1] Poncelet J V 1866 Traite des ProprieteProjectives des Figures (Paris: Gauthier-Villars) p 311 Cayley A 1858 Quart. J. Pure Appl. Math. 2 31
[2] Chang S J and Friedberg R 1988 J. Math. Phys. 29 1537 and references therein
[3] Chang S J, Crespi B and Shi K J 1993 J. Math. Phys. 34 2242
[4] Dragovic V and Radnovic M 2004 J. Phys. A 37 1269 Abenda S and Fedorov Y 2006 Lett. Math. Phys. 76 111
[5] Chang S J and Shi K J 1989 J. Math. Phys. 30798
[6] Arnold V 1984 Mathematical Methods of ClassicalMechanics (New York: Springer) p 264
[7] Guo H Y, Huang C G, Xu Z and Zhou B 2005 Chin. Phys.Lett. 22 2477
[8] Chang Z, Chen S X and Huang C G 2005 Chin. Phys.Lett. 22 791 |
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