On some classes of $3$-dimensional generalized $ (\kappa ,\mu )$-contact metric manifolds

Authors

AHMET YILDIZ
UDAY CHAND DE
AZİME ÇETİNKAYA

Abstract

The object of the present paper is to obtain a necessary and sufficient condition for a $3$-dimensional generalized $(\kappa ,\mu )$-contact metric manifold to be locally $\phi $-symmetric in the sense of Takahashi and the condition is verified by an example. Next we characterize a $3$-dimensional generalized $(\kappa ,\mu )$-contact metric manifold satisfying certain curvature conditions on the concircular curvature tensor. Finally, we construct an example of a generalized $(\kappa,\mu)$-contact metric manifold to verify Theorem $1$ of our paper.

DOI

10.3906/mat-1404-63

Keywords

Generalized $(\kappa, \mu )$-contact metric manifolds, concircular curvature tensor, $\xi $-concircularly flat, locally $\phi $-concircularly symmetric

First Page

356

Last Page

368

Recommended Citation

YILDIZ, A, DE, U. C, & ÇETİNKAYA, A (2015). On some classes of $3$-dimensional generalized $ (\kappa ,\mu )$-contact metric manifolds. Turkish Journal of Mathematics 39 (3): 356-368. https://doi.org/10.3906/mat-1404-63