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Ricci Solitons and Paracontact Geometry

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Abstract

In this article, first we prove that if a metric of a para-Sasakian manifold is a Ricci soliton, then either it is an Einstein (and V Killing) or a \(\eta \)-Einstein (and V leaves \(\varphi \) invariant) manifold. Next, we prove that if a K-paracontact metric g is a gradient Ricci soliton, then it becomes a expanding soliton which is Einstein with constant scalar curvature. Further, we study the Ricci soliton where the potential vector field V is point wise collinear with the Reeb vector field on paracontact manifold. Finally, we consider the gradient Ricci soliton on \((\kappa ,\mu )\)-paracontact manifold.

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Acknowledgements

The author is very much thankful to the referee for his or her valuable comments and suggestions for the improvement of this paper and Dr. Amalendu Ghosh for his constant support through out the preparation of the paper. The author is financially supported from BIT Mesra (funded by TEQIP-III, MHRD, Govt. of India, No. TEQIP026577).

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  1. Department of Mathematics, Birla Institute of Technology Mesra, Ranchi, 835 215, India

    Dhriti Sundar Patra

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  1. Dhriti Sundar Patra
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Correspondence to Dhriti Sundar Patra.

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Patra, D.S. Ricci Solitons and Paracontact Geometry. Mediterr. J. Math. 16, 137 (2019). https://doi.org/10.1007/s00009-019-1419-6

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  • DOI: https://doi.org/10.1007/s00009-019-1419-6

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