关于Lobachevsky空间中的椭圆台球及其测地线族
On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies
摘要：
我们推导出周期性轨道的台球在椭球内的罗巴切夫斯基空间的凯莱型条件。看来这些新的条件与以前对欧几里德情形所得到的条件具有相同的形式。我们解释这种巧合，通过使用测地线等效度量理论，并表明，罗巴切夫斯基和欧几里得椭圆台球可以自然地被认为是一个层次的可积椭圆台球的一部分。
英文摘要：
We derive Cayley's type conditions for periodical trajectories for the billiard within an ellipsoid in the Lobachevsky space. It appears that these new conditions are of the same form as those obtained before for the Euclidean case. We explain this coincidence by using theory of geodesically equivalent metrics and show that Lobachevsky and Euclidean elliptic billiards can be naturally considered as a part of a hierarchy of integrable elliptical billiards.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
