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Almost Ricci solitons and \(K\)-contact geometry

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Abstract

We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric \(g\) is \(K\)-contact and flow vector field \(X\) is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for \(X\) strict, \(g\) becomes compact Sasakian Einstein.

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Acknowledgments

The author thanks the referees for numerous constructive suggestions. This work has been supported by University Research Scholarship of the University of New Haven.

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  1. University of New Haven, West Haven, CT , 06516, USA

    Ramesh Sharma

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  1. Ramesh Sharma
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Correspondence to Ramesh Sharma.

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Communicated by A. Cap.

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Sharma, R. Almost Ricci solitons and \(K\)-contact geometry. Monatsh Math 175, 621–628 (2014). https://doi.org/10.1007/s00605-014-0657-8

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  • DOI: https://doi.org/10.1007/s00605-014-0657-8

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