Einstein warped product manifolds with 3−dimensional fiber manifolds

Einstein warped product manifolds with 3−dimensional fiber manifolds

In this paper, we consider the existence of nonconstant warping functions on a warped product manifold M = B ×f 2 F , where B is a q(> 2)−dimensional base manifold with a nonconstant scalar curvature SB (x) and F is a 3− dimensional fiber Einstein manifold and discuss that the resulting warped product manifold is an Einstein manifold, using the existence of the solution of some partial differential equation.