On Holomorphic poly-Norden Manifolds

Abstract

In this paper, we investigated a new manifold with a poly-Norden structure, which is inspired by the positive root of the equation $x^{2}-mx-1=0$. We call this new manifold as holomorphic poly-Norden manifolds. We examine some properties of the Riemann curvature tensor and give an example of this manifold. Then, we define a different connection on this manifold which is named the semisymmetric metric poly F-connection and study some properties of the curvature and torsion tensor field according to this connection.