On $(k,\mu )$-Paracontact Manifold Satisfying Some Curvature Conditions

Abstract

In this work, we studied the curvature tensors of (k,$\mu$) satisfying the conditions $\widetilde{Z}(\xi ,\alpha _{3})\cdot P=0$, $\widetilde{Z}(\xi ,\alpha _{3})\cdot S=0$, $R(\xi ,\alpha _{3})\cdot P=0$, $R(\xi ,\alpha _{3})\cdot S=0$ and $P\cdot C=0$. Besides this, we classify $(k,\mu)$-paracontact manifolds. Also we researched conformally flat and $\phi $-conformally flat a $(k,\mu )-$paracontact metric manifolds.