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

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

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