Parallel and totally geodesic hypersurfaces of 5-dimensional 2-step homogeneous nilmanifolds

Nasehi, Mehri

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 547-559

Abstract (VO)

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.

Détail

DOI : 10.1007/s10587-016-0274-x

Classification : 53C30, 53C42
Keywords: hypersurface; totally geodesic hypersurface; parallel geodesic hypersurfaces; two-step homogeneous nilmanifold

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