Metric foliations of homogeneous three-spheres
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A smooth foliation of a Riemannian manifold is metric when its leaves are locally equidistant and is homogeneous when its leaves are locally orbits of a Lie group acting by isometries. Homogeneous foliations are metric foliations, but metric foliations need not be homogeneous foliations. We prove that a homogeneous three-sphere is naturally reductive if and only if all of its metric foliations are homogeneous.
KeywordsHomogeneous spaces Naturally reductive space Metric foliations
Mathematics Subject Classification53C12 57R30 53C30
- 16.Speranca, L., Weil, S.: Metric foliations on the Euclidean space (2018). arXiv:1806.09580v1