Abstract
The current article is about almost Schouten solitons and gradient Schouten solitons on almost cosymplectic and \(\alpha \)-almost cosymplectic manifolds. Amongothers, we prove the non existence of almost Schouten solitons on a compact \((k,\mu )\)-almost cosymplectic manifold with \(k<0\). Next, we characterize \((k,\mu )\)-almost cosymplectic manifolds obeying gradient Schouten solitons. Furthermore, it is shown that if a compact \(\alpha \)-almost cosymplectic manifold admits an almost Schouten soliton, then the manifold becomes an almost cosymplectic manifold. Then we prove that a 3-dimensional cosymplectic manifold admitting a gradient Schouten soliton is either flat or the scalar curvature is constant. Finally, we build an example to demonstrate our outcome.
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Acknowledgements
We would like to thank the referee and the editor for reviewing the paper carefully and their valuable comments to improve the quality of the paper. Arpan Sardar is financially supported by UGC, Ref. ID. 4603/(CSIR-UGCNETJUNE2019).
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Arpan Sardar is financially supported by UGC, Ref. ID. 4603/(CSIR-UGCNETJUNE2019).
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Sardar, A., De, U.C. Almost Schouten solitons and almost cosymplectic manifolds. J. Geom. 114, 13 (2023). https://doi.org/10.1007/s00022-023-00674-6
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DOI: https://doi.org/10.1007/s00022-023-00674-6
Keywords
- almost schouten solitons
- gradient schouten solitons
- almost cosymplectic manifolds
- almost cosymplectic \((k,\mu )\)-manifolds