Norden structures on cotangent bundles

Abstract

We study prolongation of Norden structures on manifolds to their generalized tangent bundles and to their cotangent bundles. In particular, by using methods of generalized geometry, we prove that the cotangent bundle of a complex Norden manifold $(M,J,g)$ admits a structure of Norden manifold, $(T^{\star }(M),\tilde{J},\tilde{g})$. Moreover if $(M,J,g)$ has flat natural canonical connection then $\tilde{J}$ is integrable, that is $(T^{\star }(M),\tilde{J},\tilde{g})$ is a complex Norden manifold. Finally we prove that if $(M,J,g)$ is Kähler Norden flat then $(T^{\star }(M),\tilde{J},\tilde{g})$ is Kähler Norden flat.