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Monatshefte für Mathematik

, Volume 175, Issue 4, pp 621–628 | Cite as

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

  • Ramesh Sharma
Article

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.

Keywords

Almost Ricci soliton Conformal vector field Constant scalar curvature \(K\)-Contact metric Einstein Sasakian metric 

Mathematics Subject Classification (2010)

53C25 53C44 53C21 

Notes

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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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.University of New HavenWest HavenUSA

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