Generalized quasi-einstein manifolds in contact geometry

In this study, we investigate generalized quasi-Einstein normal metric contact pair manifolds. Initially, we deal with the elementary properties and existence of generalized quasi-Einstein normal metric contact pair manifolds. Later, we explore the generalized quasi-constant curvature of normal metric contact pair manifolds. It is proved that a normal metric contact pair manifold with generalized quasi-constant curvature is a generalized quasi-Einstein manifold. Normal metric contact pair manifolds satisfying cyclic parallel Ricci tensor and the Codazzi type of Ricci tensor are considered, and further prove that a generalized quasi-Einstein normal metric contact pair manifold does not satisfy Codazzi type of Ricci tensor. Finally, we characterize normal metric contact pair manifolds satisfying certain curvature conditions related toM-projective, conformal, and concircular curvature tensors. We show that a normal metric contact pair manifold with generalized quasi-constant curvature is locally isometric to the Hopf manifold S2n+1(1) x S1.