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Horizontal diameter of unit spheres with polar foliations and infinitesimally polar actions
International Journal of Mathematics ( IF 0.604 ) Pub Date : 2021-02-19 , DOI: 10.1142/s0129167x2150018x Yi Shi
中文翻译:
具有极性叶面和无限相似极性作用的单位球的水平直径
更新日期:2021-02-22
International Journal of Mathematics ( IF 0.604 ) Pub Date : 2021-02-19 , DOI: 10.1142/s0129167x2150018x Yi Shi
For a singular Riemannian foliation on a Riemannian manifold, a curve is called horizontal if it meets the leaves of perpendicularly. For a singular Riemannian foliation on a unit sphere , we show that if is a polar foliation or if is given by the orbits of an infinitesimally polar action, then the horizontal diameter of is , i.e. any two points in can be connected by a horizontal curve of length .
中文翻译:

具有极性叶面和无限相似极性作用的单位球的水平直径
对于奇异的黎曼叶面 在黎曼流形上,如果一条曲线与 垂直地。对于奇异的黎曼叶面 在单位球面上 ,我们证明 是极地叶或 由无限极地作用的轨道给出,然后 是 ,即中的任何两个点 可以通过长度为水平的曲线连接 。