Compact Einstein warped product manifolds

The warped product B ×f F of two Riemannian manifolds (B,gB) and (F,gF) with warping function f is the product manifold B× F equipped with the warped product metric gB + f2 gF, where is a positive function on B. It is well-known that the notion of warped products plays some important roles in differential geometry as well as in general relativity. In this paper, we will survey recent results on the existence of compact Einstein warped product Riemannian manifolds. © 2012 African Mathematical Union and Springer-Verlag Berlin Heidelberg.