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Article

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