On contact pseudo-metric manifolds satisfying a nullity condition

Abstract

In this paper, we aim to introduce and study $(\kappa, \mu)$-contact pseudo-metric manifold and prove that if the $\varphi$-sectional curvature of any point of $M$ is independent of the choice of $\varphi$-section at the point, then it is constant on $M$ and accordingly the curvature tensor. Also, we introduce generalized $(\kappa, \mu)$-contact pseudo-metric manifold and prove for $n>1$, that a non-Sasakian generalized $(\kappa, \mu)$-contact pseudo-metric manifold is a $(\kappa, \mu)$-contact pseudo-metric manifold.