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

Deepika, Andreas Arvanitoyeorgos, Ram Shankar Gupta

Published 2016-10-13Version 1

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.