We consider geodesic billiards on quadrics in . We consider the motion of a point mass inside a billiard table, that is, inside a domain lying on a quadric bounded by finitely many quadrics confocal with the given one and having angles at corner points of the boundary equal to . According to the well-known Jacobi-Chasles theorem this problem turns out to be integrable. We introduce an equivalence relation on the set of billiard tables and prove a theorem on their classification. We present a complete classification of geodesic billiards on quadrics in up to Liouville equivalence.

Bibliography: 19 titles.

中文翻译：

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三维欧几里得空间二次曲面上可积测地台球的拓扑分类

我们在 中考虑二次曲面上的测地线台球。我们考虑一个点质量在台球桌内的运动，也就是说，在一个位于二次曲面上的域内，该域由有限多个与给定的二次曲面共焦并且边界角点的角度等于。根据著名的 Jacobi-Chasles 定理，这个问题是可积的。我们在台球桌集合上引入了等价关系并证明了它们分类的定理。我们在二次曲面上提出了一个完整的测地台球分类，最高可达 Liouville 等价。

参考书目：19 题。