Israel Journal of Mathematics

, Volume 207, Issue 1, pp 361–375 | Cite as

Totally geodesic hypersurfaces of homogeneous spaces



We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped product of the Euclidean space and a homogeneous space, or (c) the twisted product of the line and a homogeneous space (with the warping/twisting function given explicitly). In the first case, F is also a Riemannian product; in the last two cases, it is a leaf of a totally geodesic homogeneous fibration. Case (c) can alternatively be characterized by the fact that M admits a Riemannian submersion onto the universal cover of the group SL(2) equipped with a particular left-invariant metric, and F is the preimage of the two-dimensional solvable totally geodesic subgroup.


Homogeneous Space Warped Product Riemannian Submersion Geodesic Submanifolds Riemannian Product 


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© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia

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