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 : 19 | Download : 4

Publication Date : 2022-04-01

Article Type : Research Paper

Abstract :In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric $insert ignore into journalissuearticles values(k,\mu );$-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric $insert ignore into journalissuearticles values(k,\mu );$-manifold with respect to the Schouten-van Kampen connection is an $\eta $-Einstein manifold. We investigate paracontact metric $insert ignore into journalissuearticles values(k,\mu );$-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 $insert ignore into journalissuearticles values(2n+1);$-dimensional paracontact metric $insert ignore into journalissuearticles values(k,\mu );$-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 $Ninsert ignore into journalissuearticles values(k);$-paracontact metric manifold or an Einstein manifold. Finally, we present some results related to almost Yamabe solitons in a paracontact metric $insert ignore into journalissuearticles values(k,\mu );$-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