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Summer 2009 Lorentz hypersurfaces in $E_1^4$ satisfying $\Delta\vec H=\alpha\vec H$
A. Arvanitoyeorgos, G. Kaimakamis, M. Magid
Illinois J. Math. 53(2): 581-590 (Summer 2009). DOI: 10.1215/ijm/1266934794

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 $\Delta\vec H=\vec0$.

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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

Information

Published: Summer 2009
First available in Project Euclid: 23 February 2010

zbMATH: 1190.53013
MathSciNet: MR2594645
Digital Object Identifier: 10.1215/ijm/1266934794

Subjects:
Primary: 53C40
Secondary: 53A07 , 53C50

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 2 • Summer 2009
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