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.
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.
WANG Yao-Xiong;FAN Heng;SHI Kang-Jie;WANG Chun;ZHANG Kai;ZENG Yu. Full Poncelet Theorem in Minkowski dS and AdS Spaces[J]. 中国物理快报, 2009, 26(1): 10201-010201.
WANG Yao-Xiong, FAN Heng, SHI Kang-Jie, WANG Chun, ZHANG Kai, ZENG Yu. Full Poncelet Theorem in Minkowski dS and AdS Spaces. Chin. Phys. Lett., 2009, 26(1): 10201-010201.
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2009, Vol. 26 
