Cut loci of submanifolds in space forms and in the geometries of Möbius and lie
Cut loci of submanifolds in space forms and in the geometries of Möbius and lie
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在空间形式和莫比乌斯几何形状中切割子流形的轨迹
DOI：
10.1007/bf02179087
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发表时间：
1995
影响因子：
0.5
通讯作者：
J. Hebda
中科院分区：
文献类型：
--
作者：
J. Hebda
适当嵌入于欧氏空间、双曲空间或球面上的子流形的切轨迹，可以用子流形的极大支撑球的集合来描述。给出了三种应用。首先证明了当子流形进行Möbius变换时，子流形切迹的拓扑是不变的。第二种是构造具有切割轨迹不可三角化点的黎曼流形的一种简单方法。第三部分研究了在李球几何变换下球的子流形切割轨迹的行为。
The cut locus of a submanifold embedded properly in Euclidean space, hyperbolic space, or the sphere has an elementary description in terms of the set of maximal supporting balls of the submanifold. Three applications are given. The first is a proof that the topology of the cut locus of a submanifold is invariant when the submanifold is subjected to a Möbius transformation. The second is a simple method for constructing Riemannian manifolds which have a point whose cut locus is nontriangulable. The third is an investigation of the behavior of the cut locus when a submanifold of a sphere is subjected to a transformation of Lie Sphere Geometry.