Some results on paracontact metric (k, mu)-manifolds with respect to the Schouten-van Kampen connection

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YÜKSEL PERKTAŞ S., De U. C., YILDIZ A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.51, no.2, pp.466-482, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15672/hujms.941744
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.466-482
  • Keywords: Schouten-van Kampen connection, paracontact metric (k, mu)-manifolds, Ricci semisymmetric, Einstein manifold, eta-Einstein manifold, solitons, RICCI SOLITONS, STRUCTURE THEOREMS, CONTACT
  • Inonu University Affiliated: No

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 g-Einstein manifold. We investigate paracontact metric (k, mu)-manifolds satisfying (sic) . (sic)(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.