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Israel Journal of Mathematics

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

Totally geodesic hypersurfaces of homogeneous spaces

  • Y. Nikolayevsky
Article

Abstract

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.

Keywords

Homogeneous Space Warped Product Riemannian Submersion Geodesic Submanifolds Riemannian Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityMelbourneAustralia

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