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Hypersurfaces of restricted type in Minkowski space

Authors:	Christos Baikoussis David Blair Bang-Yen Chen Filip Defever

Affiliation:	(1) Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece;(2) Department of Mathematics, Michigan State University, 48824 East Lansing, Michigan, USA;(3) Instituut voor Theoretische Fysica, Celestijnenlaan 200 D, 3001 Heverlee, Belgium

Abstract:	A submanifold M_n^r of Minkowski space $mathbb{E}_1^m$ is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of $mathbb{E}_1^m$ to the tangent space of M_n^r at every point of M_n^r. In this paper we completely classify hypersurfaces of restricted type in $mathbb{E}_1^{n + 1}$ . More precisely, we prove that a hypersurface of $mathbb{E}_1^m$ is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S^k × $mathbb{E}_1^{n - k}$ , S_k¹ × $mathbb{E}^{n - k}$ , H^k × $mathbb{E}^{n - k}$ , S_n¹, Hⁿ, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium.

Keywords:	53A05 53A07 53C40
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