Golden-Hessian Structures

Let (M, g) be an n-dimensional (pseudo)-Riemannian manifold and f : M -> R be a smooth function whose Hessian with respect to g is non-degenerate. One can define the associated (pseudo)-Riemannian Hessian metric h - del(2)f on M, where del is the Levi-Civita connection of g. In the present paper we investigate conditions under which the manifold M equipped with a (complex) golden structure and with the Hessian metric h is a (holomorphic) locally decomposable golden (Norden) Hessian manifold. Furthermore some examples are presented.