Geodesic
Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 547-559.

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In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces have three-dimensional centre.
DOI : 10.1007/s10587-016-0274-x
Classification : 53C30, 53C42
Mots-clés : hypersurface; totally geodesic hypersurface; parallel geodesic hypersurfaces; two-step homogeneous nilmanifold 
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Nasehi, Mehri. Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 547-559. doi : 10.1007/s10587-016-0274-x. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0274-x/

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