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Some results on almost Ricci solitons and geodesic vector fields

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Abstract

We show that a compact almost Ricci soliton whose soliton vector field is divergence-free is Einstein and its soliton vector field is Killing. Next we show that an almost Ricci soliton reduces to Ricci soliton if and only if the associated vector field is geodesic. Finally, we prove that a contact metric manifold is K-contact if and only if its Reeb vector field is geodesic.

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Acknowledgements

The author is thankful to the referee for the fact that Theorem 2 follows also from results in Barros et al. (2014) and Ghosh (2015).

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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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Sharma, R. Some results on almost Ricci solitons and geodesic vector fields. Beitr Algebra Geom 59, 289–294 (2018). https://doi.org/10.1007/s13366-017-0367-1

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  • DOI: https://doi.org/10.1007/s13366-017-0367-1

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