Golden-Hessian Structures

Abstract

Let (M, g) be an \(n-\)dimensional (pseudo)-Riemannian manifold and \( f:M\rightarrow {\mathbb {R}}\) be a smooth function whose Hessian with respect to g is non-degenerate. One can define the associated (pseudo)-Riemannian Hessian metric \(h=\nabla ^{2}f\) on M, where \(\nabla \) 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.