A classification of $N(\kappa )$-contact metric manifolds with $\mathcal{T}$-curvature tensor

Abstract

In this paper, we present a classification of $N(\kappa )$-contact metric manifolds with using some special flatness conditions on $\mathcal{T}$-curvature tensor. We examine $\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, $\xi$-$\mathcal{T}$-flat and $\phi$-$\mathcal{T}$-flat $N(\kappa )$-contact metric manifolds .Also,we consider the conditions $\mathcal{T}(\xi ,X).R=0$ and $\mathcal{T}(\xi ,X).S=0$ for the Riemannian curvature tensor $R$ and Ricci curvature tensor $S$. Thus, we obtain a classification of $N(\kappa )$-contact metric manifolds.

arXiv admin note: text overlap with arXiv:2004.02536