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arXiv · 1803.08900

Metric Foliations of Homogeneous Three-Spheres

Meera Mainkar·Benjamin Schmidt
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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.

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Meera Mainkar, Benjamin Schmidt. 2018-03-23. Metric Foliations of Homogeneous Three-Spheres. https://arxiv.org/abs/1803.08900

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