On N(k)-quasi Einstein Manifolds Satisfying Some Conditions

In this paper, we study -curvature tensor on -quasi Einstein manifolds. The tensor ​ is defined as a modification of the Riemannian curvature tensor involving the Ricci operator. Several of its basic properties are first derived with respect to the structure vector field , the associated ۱-form , and the Riemannian metric . Using these relations, we investigate curvature conditions involving . In particular, we consider the condition and . All the results obtained are in the form of necessary and sufficient conditions. ۲۰۱۰ AMS Classification: ۵۳C۲۵

کلیدواژه ها:

k-nullity distribution ، Quasi Einstein manifold ، N(k) -quasi Einstein manifold ، W۸-curvature tensor