On the Gauss map of ruled surfaces in a 3-dimensional minkowski space

Abstract

Relative to Takahashi's theorem [9] for minimal submanifolds, the idea of submanifolds of finite type in a Euclidean space was introduced by Chen [2] and the theory is recently greatly developed. Let x : M^Rn+1 be an isometric immersion of n-dimensional Riemannian manifold into an (n+l)-dimensional Euclidean space Rn+1 and A the Laplacian on M. As a generalization of Takahashi's theorem for the case of hypersurfaces, Garay [4] considered the hypersurface satisfying the condition Ax=Ax, where A denotes the constant diagonal matrix of order n + 1. On the other hand, let x : M~^Rm be an isometric immersion of a compact oriented ^-dimensional Riemannian manifold into Rm. For a generalized Gauss