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| Paper IPM / M / 127 |
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| Abstract: | |
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In this paper we study hypersurfaces Msn
in \BbbR1n+1 (or in \BbbRn+1) verifying the equation ∆x = Ax+B and the condition that the principal
curvatures of the surface is not (−n ∈ ) times the mean curvature at the points where the mean curvature is nonzero. We prove that the mean curvature of the surface is constant and as a result, either Msn has zero mean curvature or when Msn has at most two different principal curvatures, it is isoparametric. Here Msn is a (pseudo) Riemannian manifold with metric of signature s,s=0,1,\BbbR1n+1 is the (n+1)-dimensional flat Lorentzian space, A is an endomorphism of \BbbR1n+1 and B ∈ \BbbR1n+1, ∆ is the Laplacian operator on Msn, x: Msn → \BbbR1n+1 is an isometric immersion. Download TeX format |
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