A class of Kaehler Einstein structures on the cotangent bundle

We use some natural lifts defined on the cotangent bundle TM 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 TM 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 Kaehlerian. Combining the obtained results we get a family of Kaehlerian structures on TM, depending on two essential parameters. Next we study three conditions under which the considered Kaehlerian structures are Einstein. In one of the obtained cases we get that (TM,G,J) has constant holomorphic curvature.