A classiffication of biharmonic hypersurfaces in the Minkowski spaces of arbitrary dimension

Year 2016, Volume: 45 Issue: 4, 1125 - 1134, 01.08.2016

Nurettin Cenk Turgay

Abstract

In this paper we study hypersurfaces with the mean curvature function
H satisfying $\langle \nabla H, \nabla H\rangle $ in a Minkowski space of arbitrary dimen-
sion. First, we obtain some conditions satised by connection forms of
biconservative hypersurfaces with the mean curvature function whose
gradient is light-like. Then, we use these results to get a classication of
biharmonic hypersurfaces. In particular, we prove that if a hypersurface
is biharmonic, then it must have at least 6 distinct principal curvatures
under the hypothesis of having mean curvature function satisfying the
condition above.

Keywords

biharmonic submanifolds, Lorentzian hypersurfaces, biconservative hypersurfaces, finite type submanifolds.

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