论文标题
在双曲线上的地球散射和knörrer的地图
Geodesic scattering on hyperboloids and Knörrer's map
论文作者
论文摘要
我们使用Moser和Knörrer的结果对大地学对四边形和经典Neumann系统解决方案之间的关系，以明确描述倍曲底上的地球散射。 我们解释了Knörrer的重新测量与Tabachnikov和Matveev和Topalov独立独立的Quadrics的相同指标的相同指标的关系，从而提供了新的结果证明。我们表明，在投影上等效的度量标准是定期的，这是倍曲面的投影闭合，并将Knörrer的地图扩展到此封闭。
We use the results of Moser and Knörrer on relations between geodesics on quadrics and solutions of the classical Neumann system to describe explicitly the geodesic scattering on hyperboloids. We explain the relation of Knörrer's reparametrisation with projectively equivalent metrics on quadrics introduced by Tabachnikov and independently by Matveev and Topalov, giving a new proof of their result. We show that the projectively equivalent metric is regular on the projective closure of hyperboloids and extend Knörrer's map to this closure.
