  We obtain a locally symmetric Kaehler Einstein structure on the cotangent
bundle of a Riemannian manifold of negative constant sectional curvature.
Similar results are obtained on a tube around zero section in the cotangent
bundle, in the case of a Riemannian manifold of positive constant sectional
curvature. The obtained Kaehler Einstein structures cannot have constant
holomorphic sectional curvature.
