A class of Kahler Einstein structures on the cotangent bundle

We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M, g) in order to construct an almost Hermitian structure (G, J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and the coefficients as well as their derivatives, involved in its definition, do fulfill a certain algebraic relation. Next one obtains the condition that must be fulfilled in the case where the obtained almost Hermitian structure is almost Kahlerian. Combining the obtained results we get a family of Kahlerian structures on T*M, depending on two essential parameters. Next we study three conditions under which the considered Kahlerian structures are Einstein. In one of the obtained cases we get that (T*M, G, J) has constant holomorphic curvature.