Interaction of Codazzi Pairs with Almost Para Norden Manifolds

Abstract

In this paper, we research some properties of Codazzi pairs on almost para Norden manifolds. Let (M2n, φ, g, G) be an almost para Norden manifold. Firstly, g-conjugate connection, G-conjugate connection and φ-conjugate connection of a linear connection ∇ on M2n denoted by ∇∗, ∇† and ∇φ are defined and it is demonstrated that on the spaces of linear connections, (id, ∗, †, φ) acts as the four-element Klein group. We also searched some properties of these three types conjugate connections. Then, Codazzi pairs (∇, φ), (∇, g) and (∇, G) are introduced and some properties of them are given. Let R, R∗ and R† are (0, 4)-curvature tensors of conjugate connections ∇, ∇∗ and ∇†, respectively. The relationship among the curvature tensors is investigated. The condition of Nφ = 0 is obtained, where Nφ is Nijenhuis tensor field on M2n and it is known that the condition of integrability of almost para complex structure φ is Nφ = 0. In addition, Tachibana operator is applied to the pure metric g and a necessary and sufficient condition (M, φ, g, G) being a para Kahler Norden manifold is found. Finally, we examine φ-invariant linear connections and statistical manifolds. © MatDer.