Special class of higher dimensional stationary manifold

Abstract

In this paper, we classify a special class of higher dimensional stationary manifolds. We consider an n dimensional manifold N with metric ds^2=g^ijdxidxj which is embedded to an n + 1 dimensional stationary manifold M with metric ds2=εω2(dt+αidxi)2+ω2g^ijdxidxj. The submanifold is taken to be almost complex manifold with parallel and integrable almost complex structure where dα is its Kähler form. We will demonstrate that the sub-manifold N is maximally symmetric space if manifold M is maximally symmetric space, otherwise the sub-manifold N is Einstein space if manifold M is Einstein space.