Ricci Solitons on Pseudosymmetric $(\kappa,\mu)$-Paracontact Metric Manifolds

Abstract

The object of the present paper is to study some types of Ricci pseudosymmetric $(\kappa,\mu)$-paracontact metric manifolds whose metric admits Ricci soliton. We researched the conditions when Ricci soliton on Ricci pseudosymmetric, concircular Ricci pseudosymmetric, $W_3$-Ricci pseudosymmetric, Weyly projective Ricci pseudosymmetric and conharmonic Ricci pseudosmettric conditions on a $(\kappa,\mu)$-paracontact metric manifold. According to these conditions, we have evaluated the manifold to be shrinking, steady and expanding. Finally, we have also constructed a non-trivial example of $(\kappa,\mu)$-paracontact metric manifolds whose metric admits Ricci soliton and found the functions for the Ricci pseudosymmetric conditions.

Keywords

• Paracontact metric manifold
• $(\kappa, \mu)$-paracontact metric manifold
• Ricci soliton and pseudosymmetric manifolds

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