Metric foliations of homogeneous three-spheres

Meera Mainkar, Benjamin Schmidt

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)73-84
Number of pages12
JournalGeometriae Dedicata
Issue number1
StatePublished - Dec 1 2019


  • Homogeneous spaces
  • Metric foliations
  • Naturally reductive space


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