- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 2
- Some results on paracontact metric $(k,\mu)$-manifolds with respect to the Schouten-van Kampen conne...
Some results on paracontact metric $(k,\mu)$-manifolds with respect to the Schouten-van Kampen connection
Authors : Selcen Yüksel Perktaş, U. C. De, Ahmet Yildiz
Pages : 466-482
Doi:10.15672/hujms.941744
View : 16 | Download : 5
Publication Date : 2022-04-01
Article Type : Research
Abstract :In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric $(k,\mu )$-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection is an $\eta $-Einstein manifold. We investigate paracontact metric $(k,\mu )$-manifolds satisfying $\breve{Q}\cdot \breve{R}_{cur}=0$\ with respect to the Schouten-van Kampen connection. Also, we show that there does not exist an almost Ricci soliton in a $(2n+1)$-dimensional paracontact metric $(k,\mu )$-manifold with respect to the Schouten-van Kampen connection such that $k>-1$ or $k<-1$. In case of the metric is being an almost gradient Ricci soliton with respect to the Schouten-van Kampen connection, then we state that the manifold is either $N(k)$-paracontact metric manifold or an Einstein manifold. Finally, we present some results related to almost Yamabe solitons in a paracontact metric $(k,\mu )$-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results.Keywords : Schouten-van Kampen connection, Ricci semisymmetric, Einstein manifold, $eta $-Einstein manifold, solitons, paracontact metric $(k, mu )$-manifolds