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Ricci Almost Solitons on Three-Dimensional Quasi-Sasakian Manifolds

  • Avijit Sarkar
  • Amit Sil
  • Avijit Kumar Paul
Research Article
  • 30 Downloads

Abstract

In this paper it is shown that a three-dimensional non-cosymplectic quasi-Sasakian manifold admitting Ricci almost soliton is locally \(\phi \)-symmetric. It is proved that a Ricci almost soliton on a three-dimensional quasi-Sasakian manifold reduces to a Ricci soliton. It is also proved that if a three-dimensional non-cosymplectic quasi-Sasakian manifold admits gradient Ricci soliton, then the potential function is invariant in the orthogonal distribution of the Reeb vector field \(\xi\). We also improve some previous results regarding gradient Ricci soliton on three-dimensional quasi-Sasakian manifolds. An illustrative example is given to support the obtained results.

Keywords

Ricci flow Ricci solitons Locally \(\phi \) symmetric Gradient Ricci solitons Quasi-Sasakian manifolds 

Mathematics Subject Classification

53 C 15 53 D 15 

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Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KalyaniKalyani, NadiaIndia

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