Abstract
A hypersurface $M_1^3$ in the four-dimensional pseudo-Euclidean space $E_1^4$ is called a Lorentz hypersurface if its normal vector is space-like. We show that if the mean curvature vector field of $M_1^3$ satisfies the equation $\Delta\vec H=\alpha\vec H$ ($\alpha$ a constant), then $M_1^3$ has constant mean curvature. This equation is a natural generalization of the biharmonic submanifold equation $\Delta\vec H=\vec0$.
Citation
A. Arvanitoyeorgos. G. Kaimakamis. M. Magid. "Lorentz hypersurfaces in $E_1^4$ satisfying $\Delta\vec H=\alpha\vec H$." Illinois J. Math. 53 (2) 581 - 590, Summer 2009. https://doi.org/10.1215/ijm/1266934794
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