SOME PROPERTIES OF $N(k)$-QUASI EINSTEIN MANIFOLDS

In this paper, an example of an N (k)-quasi Einstein manifold with closed associated 1-form is given.Also we show that if a quasi Einstein manifold (M n 1 1 , g 1 ) and an Einstein manifold (M n 2 2 , g 2 ) satisfy a certain condition, then the Riemannian product manifold (M n , g) = (M n 1 1 × M n 2 2 , g 1 + g 2 ) is a quasi Einstein manifold.In particular, in N (k)-quasi Einstein case, we show that there exists a quasi Einstein product manifold (M n , g) = (M n 1 1 × M n 2 2 , g 1 + g 2 ) but not an N (k)-quasi Einstein manifold, which consists of an N (k)-quasi Einstein manifold (M n 1 1 , g 1 ) and an Einstein manifold (M n 2 2 , g 2 ) satisfying the certain condition.Finally we study an N (k)-quasi Einstein manifold satisfying the condition R(U, X) • G = 0.