N(k)-paracontact three metric as a Eta-Ricci soliton

Authors

  • D. Kar University of Calcutta, West Bengal, India
  • P. Majhi University of Calcutta, West Bengal, India

DOI:

https://doi.org/10.31926/but.mif.2020.13.62.2.16

Keywords:

Paracontact structure, Eta-Ricci soliton, constant curvature, Killing vector field, infinitesimal automorphism

Abstract

In this paper, we study Eta-Ricci soliton (η-Ricci soliton) on three dimensional N(k)-paracontact metric manifolds. We prove that the scalar curvature of an N(k)-paracontact metric manifold admitting η-Ricci solitons is constant and the manifold is of constant curvature k. Also, we prove that such manifolds are Einstein. Moreover, we show the condition of that the η-Ricci soliton to be expanding, steady, or shrinking. In such a case we prove that the potential vector field is Killing vector field. Also, we show that the potential vector field is an infinitesimal automorphism or it leaves the structure tensor in the direction perpendicular to the Reeb vector field ξ. Finally, we illustrate an example of a three dimensional N(k)-paracontact metric manifold admitting an η-Ricci soliton.

Author Biographies

D. Kar, University of Calcutta, West Bengal, India

Department of Pure Mathematics, 35, Ballygunge Circular Road, Kolkata-700019

P. Majhi, University of Calcutta, West Bengal, India

Department of Pure Mathematics, 35, Ballygunge Circular Road, Kolkata-700019

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Published

2021-01-22

Issue

Section

MATHEMATICS