Special Class of Higher Dimensional Stationary Manifold.

In this paper, we classify a special class of higher dimensional stationary manifolds. We consider an n dimensional manifold N with metric dŝ2 =ĝij dxi dxj which is embedded to an n + 1 dimensional stationary manifold M with metric ds2 = ε/ω2(dt + αdxi)2+ω2 ĝij dxi dxj . 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. [ABSTRACT FROM AUTHOR]