Metric Foliations of Homogeneous Three-Spheres
Differential Geometry
2019-01-23 v2
Abstract
A smooth foliation of a Riemannian manifold is metric when its leaves are locally equidistant and is homogenous when its leaves are locally orbits of a Lie group acting by isometries. Homogenous foliations are metric foliations, but metric foliations need not be homogenous foliations. We prove that a homogenous three-sphere is naturally reductive if and only if all of its metric foliations are homogenous.
Keywords
Cite
@article{arxiv.1803.08900,
title = {Metric Foliations of Homogeneous Three-Spheres},
author = {Meera Mainkar and Benjamin Schmidt},
journal= {arXiv preprint arXiv:1803.08900},
year = {2019}
}
Comments
This paper has been accepted for publication in Geometriae Dedicata