Some results on almost Ricci solitons and geodesic vector fields

Original Paper
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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.

Keywords

Almost Ricci soliton Contact metric structure K-contact Einstein Sasakian 

Mathematics Subject Classification

53C25 53C44 53C21 

Notes

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).

References

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Copyright information

© The Managing Editors 2017

Authors and Affiliations

  1. 1.University of New HavenWest HavenUSA

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