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Sasakian metrics as generalized \(\eta \)-Ricci soliton

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Abstract

In this paper, we consider Sasakian metric as a proper \(\eta \)-Ricci almost soliton and prove that it is isometric to a unit sphere \(S^{2n+1}\), provided the dimension of the manifold is greater than 3. Next, we prove that if a Sasakian manifold admitting a generalized \(\eta \)-Ricci soliton whose potential vector field is a contact vector field is \(\eta \)-Einstein and the potential vector field is Killing. Finally, we prove that a complete Sasakian manifold of dimension greater than 3 is isometric to a unit sphere if it admits a non-trivial gradient generalized \(\eta \)-Ricci soliton.

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Acknowledgements

The author is very much thankful to the reviewers for their useful comments towards the improvement of the presentation of the paper.

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Correspondence to Amalendu Ghosh.

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Ghosh, A. Sasakian metrics as generalized \(\eta \)-Ricci soliton. Period Math Hung 86, 139–151 (2023). https://doi.org/10.1007/s10998-022-00462-w

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