Certain Results On $N(\mathrm{K})$-contact Metric Manifolds

Abstract

In this paper, $N(\kappa )$-contact metric manifolds satisfying the conditions $\tilde{C}(\xi ,X)\cdot \tilde{C}=0$, $\tilde{C}(\xi ,X)\cdot R=0$, $\tilde{C}(\xi ,X)\cdot S=0$, $\tilde{C}(\xi ,X)\cdot C=0$, $C\cdot S=0$ 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.

12 pages

References in corpus (1)

• On warped product manifolds satisfying some pseudosymmetric type conditions