International Journal of Mathematics ( IF 0.604 ) Pub Date : 2021-02-19 , DOI: 10.1142/s0129167x2150018x
Yi Shi

For a singular Riemannian foliation $ℱ$ on a Riemannian manifold, a curve is called horizontal if it meets the leaves of $ℱ$ perpendicularly. For a singular Riemannian foliation $ℱ$ on a unit sphere $𝕊n$, we show that if $ℱ$ is a polar foliation or if $ℱ$ is given by the orbits of an infinitesimally polar action, then the horizontal diameter of $𝕊n$ is $π$, i.e. any two points in $𝕊n$ can be connected by a horizontal curve of length $≤π$.

down
wechat
bug