On the Einstein standard stationary space-times

Abstract

In this paper, we study Einstein standard stationary space-times [Formula: see text] of dimension [Formula: see text] with [Formula: see text] is conformal on the space-like hypersurface [Formula: see text]. When [Formula: see text] is assumed to be connected and complete, we give a criterion so that [Formula: see text] is Einstein. In particular, we show that if [Formula: see text] is Einstein and [Formula: see text] is complete and connected, then the scalar curvature of [Formula: see text] and that of [Formula: see text] are non-positive and [Formula: see text] is Killing with respect to [Formula: see text].