On the horizontal diameter of the unit sphere

摘要

For a singular Riemannian foliation on a Riemannian manifold M, 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 satisfies some properties, then the horizontal diameter of is , i.e., any two points in can be connected by a horizontal curve of length = pi.