n-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection

Abstract

We consider a generalization of a Ricci soliton as $ \eta $-Ricci-Bourguignon solitons on a Riemannian manifold endowed with a semi-symmetric metric and semi-symmetric non-metric connection. We find some properties of $ \eta $-Ricci-Bourguignon soliton on Riemannian manifolds equipped with a semi-symmetric metric and semi-symmetric non-metric connection when the potential vector field is torse-forming with respect to a semi-symmetric metric and semi-symmetric non-metric connection.

Keywords

• n-ricciection
• torse-forming vector field
• quasi-einstein manifold
• hyper-generalized quasi-einstein manifold-bourguignon soliton
• semi-symmetric metric connection
• semi-symmetric non-metric conn