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m-quasi-Einstein metric and contact geometry

  • Amalendu GhoshEmail author
Original Paper
  • 5 Downloads

Abstract

We study m-quasi-Einstein metric in the framework of contact metric manifolds. The existence of such metric has been confirmed on the class of \( \eta \)-Einstein K-contact manifold, in which the potential vector field V is a constant multiple of the Reeb vector field \(\xi \). Next, we consider closed m-quasi-Einstein metric on a complete K-contact manifold and prove that it is Sasakian and Einstein provided \(m\ne 1\). We also proved that, if a K-contact manifold M admits an m-quasi-Einstein metric such that the potential vector field V is conformal, then V becomes Killing and M is \( \eta \)-Einstein. Finally, we obtain a couple of results on a contact metric manifold M admitting an m-quasi-Einstein metric, whose potential vector field is a point wise collinear with the Reeb vector field.

Keywords

m-quasi-Einstein metric Ricci soliton Gradient Ricci soliton Contact metric manifold K-contact manifold 

Mathematics Subject Classification

53C25 53C15 53D10 

Notes

Acknowledgements

The author expresses his sincere thanks to the referee for offering many valuable suggestions towards the improvement of the paper.

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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Department of MathematicsChandernagore CollegeChandannagarIndia

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