SUBMANIFOLDS IN DE SITTER SPACE-TIME SATISFYING DELTA-H=LAMBDA-H

In [3] the author initiated the study of submanifolds whose mean curvature vector H is an eigenvector of the Laplacian Delta and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type. The classification of surfaces with Delta H = lambda H in a Euclidean 3-space was done by the author in 1988. Moreover, in [4] the author classified such submanifolds in hyperbolic spaces. In this article we study this problem for space-like submanifolds of the Minkowski space-time E(1)(m) when the submanifolds lie in a de Sitter space-time. As a result, we characterize and classify such submanifolds in de Sitter space-times.