- Turkish Journal of Mathematics
- Vol: 39 Issue: 3
- On some classes of $3$-dimensional generalized $ (\kappa ,\mu )$-contact metric manifolds
On some classes of $3$-dimensional generalized $ (\kappa ,\mu )$-contact metric manifolds
Authors : Ahmet Yildiz, Uday Chand De, Azime Çetinkaya
Pages : 356-368
Doi:10.3906/mat-1404-63
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Generalized $(kappa, mu )$-contact metric manifolds, concircular curvature tensor, $xi $-concircularly flat, locally $phi $-concircularly symmetric