Abstract:
In the present paper we study certain symmetry conditions and some types of solitons on paracontact metric (k, µ)-manifolds with respect to the Schouten-van Kampen connection. We prove that a Ricci semisymmetric paracontact metric (k, µ)-manifold with respect to the Schouten-van Kampen connection is an η-Einstein manifold. We investigate paracontact metric (k, µ)-manifolds satisfying˘Q ·˘Rcur = 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, µ)-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, µ)-manifold equipped with the Schouten-van Kampen connection and construct an example which verifies some of our results. © 2022, Hacettepe University. All rights reserved.