A HARMONIC ENDOMORPHISM IN A SEMI-RIEMANNIAN CONTEXT

On the total space of the cotangent bundle T* M of a Riemannian manifold (M, h) we consider the natural Riemann extension (g) over bar with respect to the Levi-Civita connection of h. In this setting, we construct on T double dagger M a new para-complex structure P, whose harmonicity with respect to (g) over bar is characterized here by using the reduction of (g) over bar to the (classical) Riemann extension.