$ \eta $-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection

Yusuf Dogru; Yusuf Dogru

doi:10.3934/math.2023603

AIMS Mathematics

2023, Volume 8, Issue 5: 11943-11952. doi: 10.3934/math.2023603

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$ \eta $-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection

Yusuf Dogru ^,

Air Training Command, Konak, İzmir, Turkey

Received: 23 January 2023 Revised: 10 March 2023 Accepted: 16 March 2023 Published: 20 March 2023
MSC : 35Q51, 53C07, 53C25

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.
Citation: Yusuf Dogru. $ \eta $-Ricci-Bourguignon solitons with a semi-symmetric metric and semi-symmetric non-metric connection[J]. AIMS Mathematics, 2023, 8(5): 11943-11952. doi: 10.3934/math.2023603

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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.

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