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arXiv · 1610.04095

Lorentz Hypersurfaces satisfying $\triangle \vec {H}= \alpha \vec {H}$ with non diagonal shape operator

Deepika·Andreas Arvanitoyeorgos·Ram Shankar Gupta
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Abstract

We study Lorentz hypersurfaces $M_{1}^{n}$ in $E_{1}^{n+1}$ satisfying $\triangle \vec {H}= \alpha \vec {H}$ with non diagonal shape operator, having complex eigenvalues. We prove that every such Lorentz hypersurface in $E_{1}^{n+1}$ having at most five distinct principal curvatures has constant mean curvature.

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Deepika, Andreas Arvanitoyeorgos, Ram Shankar Gupta. 2016-10-13. Lorentz Hypersurfaces satisfying $\triangle \vec {H}= \alpha \vec {H}$ with non diagonal shape operator. https://doi.org/10.1007/s40863-016-0056-2

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