Open AccessN(k)-paracontact three metric as a Eta-Ricci soliton
Author(s) -
Debabrata Kar,
Pradip Majhi
Publication year - 2020
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics, informatics, physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.203
H-Index - 5
eISSN - 2065-216X
pISSN - 2065-2151
DOI - 10.31926/but.mif.2020.13.62.2.16
Subject(s) - ricci curvature , scalar curvature , mathematics , vector field , mathematical physics , soliton , riemann curvature tensor , manifold (fluid mechanics) , mathematical analysis , curvature , physics , geometry , quantum mechanics , mechanical engineering , nonlinear system , engineering
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