# Certain Results On $N(\Kappa)$-contact Metric Manifolds

## TL;DR

This paper classifies certain $N(ppa)$-contact metric manifolds satisfying specific curvature conditions, revealing their geometric structure and providing an example.

## Contribution

It provides a classification of $N(ppa)$-contact metric manifolds under various curvature constraints, including Weyl-pseudosymmetry.

## Key findings

- Weyl-pseudosymmetric $N(ppa)$-contact metric manifolds are either locally isometric to a product space or $ta$-Einstein.
- The paper offers explicit classifications based on curvature conditions.
- An explicit example of such a manifold is constructed.

## Abstract

In this paper, $N(\kappa)$-contact metric manifolds satisfying the conditions $\widetilde{C}(\xi,X)\cdot\widetilde{C}=0$, $\widetilde{C}(\xi,X)\cdot R=0$, $\widetilde{C}(\xi,X)\cdot S=0$, $\widetilde{C}(\xi,X)\cdot C=0$, $C\cdot S=0$ and $R\cdot C=f_{C}Q(g,C)$ have been investigated and obtained their classification. Among others it is shown that a Weyl-pseudosymmetric $N(\kappa)$-contact metric manifold is either locally isometric to the Riemannian product $E^{n+1}(0)\times S^{n}(4)$ or an $\eta$-Einstein manifold. Finally, an example is given.