Metric foliations of homogeneous three-spheres

  • Meera Mainkar
  • Benjamin SchmidtEmail author
Original Paper


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.


Homogeneous spaces Naturally reductive space Metric foliations 

Mathematics Subject Classification

53C12 57R30 53C30 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsCentral Michigan UniversityMount PleasantUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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