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

Year 2023, Volume: 15 Issue: 1, 171 - 179, 30.06.2023

Pakize Uygun , Mehmet Atçeken

https://doi.org/10.47000/tjmcs.1153650

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.

Keywords

$(k,\mu)$-Paracontact manifold, Einstein manifold, Weyl projective curvature tensor, conformal curvature tensor, concircular curvature tensor

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