Higher dimensional maximally symmetric stationary manifold with pure gauge condition and codimension one flat submanifold

Abstract

An n dimensional flat manifold N is embedded into an n+1 dimensional stationary manifold M. The metric of M is derived from a general form of stationary manifold. By taking several assumption, such as 1) the ambient manifold M to be maximally symmetric space and satisfying a pure gauge condition, and 2) the submanifold is taken to be flat, then we find the solution that satisfies Ricci scalar of N. Moreover, we determine whether the solution is compatible with the Ricci and Riemann tensor of manifold N depending on the dimension.