Some properties of Codazzi pairs on para norden manifolds

In this thesis, firstly, let 𝑔 be a para Norden metric, 𝜑 be a para complex structure, 𝐺 be a twin para Norden metric and ∇ be a linear connection on 𝑀2𝑛 differentiable manifold, ∇𝜑,∇∗ and ∇†are conjugate connections which are linear with respect to 𝜑,𝑔and 𝐺are defined. These connections are shown to provide the properties of Klein-4 group. Let the curvature tensors of the connections ∇,∇∗ and ∇† be 𝑅,𝑅∗ and 𝑅†, respectively,the relationship between these curvature tensors is found. Later, (∇,𝜑),(∇,𝑔)and (∇,𝐺)Codazzi pairs are defined on (𝑀2𝑛,𝜑,𝑔,𝐺)and some properties of these pairs are examined. The necessary and sufficient condition for (𝑀2𝑛,𝜑,𝑔,𝐺)to be a para Kahler Norden is investigated. Finally, properties of 𝜑−invariant linear connection and statistical manifold are studied.