A NOTE ON THE SILVER HESSIAN STRUCTURE

Abstract

In this paper, we study locally decomposable Silver-Hessian manifolds and holomorphic Silver Norden Hessian manifolds. We investigate that if the smooth function f:M→R is decomposable, then the triplet (M,Θ,∇^2 f ) is a locally decomposable Silver Hessian manifold, where Θ is a Silver structure and ∇ represents the Levi-Civita Connection of g. We obtain some conditions under which the manifold Mis associated with Hessian metric h and complex Silver structure. Moreover, we investigate the twin Norden Silver Hessian metric for a Kaehler-Norden Silver Hessian manifold.