Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry

• Published in: Open mathematics (Warsaw, Poland) Vol. 20; no. 1; pp. 574 - 589
• Main Authors: Li, Yanlin, Dey, Santu, Pahan, Sampa, Ali, Akram
• Format: Journal Article
• Language: English
• Published: Warsaw De Gruyter 09.08.2022; De Gruyter Poland
• Subjects: 53C15; 53C25; 53D15; conformal η-Ricci soliton; Einstein manifold; Fields (mathematics); infinitesimal contact transformation; Kenmotsu manifold; Manifolds (mathematics); para-cosymplectic manifold; Solitary waves
• ISSN: 2391-5455; 2391-5455
• DOI: 10.1515/math-2022-0048

We prove that if an -Einstein para-Kenmotsu manifold admits a conformal -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal -Ricci soliton is Einstein if its potential vector field is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal -Ricci soliton and satisfy our results. We also have studied conformal -Ricci soliton in three-dimensional para-cosymplectic manifolds.