ON PRODUCT RIEMANNIAN MANIFOLD

In this paper, we show that in the Riemannian product manifolds (M=M1*M2,g=g1 g2), if M is a quasi Einstein manifold then (M1,g2) and (M2,g2) are quasi Einstein manifold and the covers is true if M1 and M2 are Einstein manifold with the same scalar curvatures.

Keywords:

Product Riemannian manifold , Einstein manifolds , quasi Einstein manifolds