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arXiv · 1412.5479

Biharmonic hypersurfaces in space forms with three distinct principal curvatures

Ram Shankar Gupta
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Abstract

In this paper, we have studied biharmonic hypersurfaces in space form $\bar{M}^{n+1}(c)$ with constant sectional curvature $c$. We have obtained that biharmonic hypersurfaces $M^{n}$ with at most three distinct principal curvatures in $\bar{M}^{n+1}(c)$ has constant mean curvature. We also obtain the full classification of biharmonic hypersurfaces with at most three distinct principal curvatures in arbitrary dimension space form $\bar{M}^{n+1}(c)$.

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Ram Shankar Gupta. 2014-12-17. Biharmonic hypersurfaces in space forms with three distinct principal curvatures. https://arxiv.org/abs/1412.5479

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