Displaying similar documents to “Parallel and totally geodesic hypersurfaces of solvable Lie groups”

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

Mehri Nasehi (2016)

Czechoslovak Mathematical Journal

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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...

Foliations of lightlike hypersurfaces and their physical interpretation

Krishan Duggal (2012)

Open Mathematics

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This paper deals with a family of lightlike (null) hypersurfaces (H u) of a Lorentzian manifold M such that each null normal vector ℓ of H u is not entirely in H u, but, is defined in some open subset of M around H u. Although the family (H u) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H u) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ...