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

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Hacettepe Journal of Mathematics and Statistics
Volume:45 Issue:4
A classiffication of biharmonic hypersurfaces in the Minkowski spaces of arbitrary dimension

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

Authors : Nurettin Cenk TURGAY

Pages : 1125-1134

View : 49 | Download : 10

Publication Date : 2016-08-01

Article Type : Research Paper

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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