Ricci tensor on normal metric contact pair manifolds

Abstract

In this paper we study NMCP manifolds, which are (2p+2q+2)?dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the ??Ricci tensor. We prove that a??Ricci-semi-symmetric NMCP manifold is ??Ricci-flat, and that a ??generalized quasi-Einstein NMCP manifold cannot be ??Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space © Balkan Society of Geometers, Geometry Balkan Press 2022