Ahmet YILDIZ, Uday Chand DE, Azime ÇETİNKAYA

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

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.

Anahtar Kelimeler:

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

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

Keywords:

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

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