Properties of 2-dimensional space-like ruled surfaces in the Minkowski space $Bbb{R}^n_1$

Abstract

In this paper we find new characteristic properties for 2-dimensional ruled surface M in $Bbb{R}^n_1$ and give the sufficient and necessary conditions for which the space-like ruled surface M is to be total geodesic. In addition, some characterisation which is the well-known for the ruled surfaces in the Euclidean 3-space was generalized for the space-like ruled surfaces in $Bbb{R}^n_1$.