On Holomorphic poly-Norden Manifolds

Abstract

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