Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

Yanlin Li; Dipen Ganguly; Santu Dey; Arindam Bhattacharyya; Yanlin Li; Dipen Ganguly; Santu Dey; Arindam Bhattacharyya

doi:10.3934/math.2022300

AIMS Mathematics

2022, Volume 7, Issue 4: 5408-5430. doi: 10.3934/math.2022300

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Research article

Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds

1.
School of Mathematics, Hangzhou Normal University, Hangzhou, 311121, China
2.
Department of Mathematics, Jadavpur University, Kolkata 700032, India
3.
Department of Mathematics, Bidhan Chandra College, Asansol-4, West Bengal 713304, India

Received: 13 October 2021 Revised: 19 December 2021 Accepted: 31 December 2021 Published: 06 January 2022
MSC : 53C15, 53C25, 53D10

The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal $ \eta $-Ricci soliton on $ \epsilon $-Kenmotsu manifold.
- Ricci soliton,
- conformal Ricci soliton,
- conformal $ \eta $-Ricci soliton,
- $ \epsilon $-Kenmotsu manifold,
- concircular curvature tensor,
- codazzi type Ricci tensor
Citation: Yanlin Li, Dipen Ganguly, Santu Dey, Arindam Bhattacharyya. Conformal $ \eta $-Ricci solitons within the framework of indefinite Kenmotsu manifolds[J]. AIMS Mathematics, 2022, 7(4): 5408-5430. doi: 10.3934/math.2022300

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Abstract

The present paper is to deliberate the class of $ \epsilon $-Kenmotsu manifolds which admits conformal $ \eta $-Ricci soliton. Here, we study some special types of Ricci tensor in connection with the conformal $ \eta $-Ricci soliton of $ \epsilon $-Kenmotsu manifolds. Moving further, we investigate some curvature conditions admitting conformal $ \eta $-Ricci solitons on $ \epsilon $-Kenmotsu manifolds. Next, we consider gradient conformal $ \eta $-Ricci solitons and we present a characterization of the potential function. Finally, we develop an illustrative example for the existence of conformal $ \eta $-Ricci soliton on $ \epsilon $-Kenmotsu manifold.

References

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