Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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∗-RICCI SOLITONS AND ∗-GRADIENT RICCI SOLITONS ON 3-DIMENSIONAL TRANS-SASAKIAN MANIFOLDS

  • Dey, Dibakar (Department of Pure Mathematics University of Calcutta) ;
  • Majhi, Pradip (Department of Pure Mathematics University of Calcutta)
  • Received : 2019.04.01
  • Accepted : 2019.09.26
  • Published : 2020.04.30
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Abstract

The object of the present paper is to characterize 3-dimensional trans-Sasakian manifolds of type (α, β) admitting ∗-Ricci solitons and ∗-gradient Ricci solitons. Under certain restrictions on the smooth functions α and β, we have proved that a trans-Sasakian 3-manifold of type (α, β) admitting a ∗-Ricci soliton reduces to a β-Kenmotsu manifold and admitting a ∗-gradient Ricci soliton is either flat or ∗-Einstein or it becomes a β-Kenmotsu manifold. Also an illustrative example is presented to verify our results.

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References

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