On three-dimensional (m,ρ)-quasi-Einstein N(κ)-contact metric manifold

Abstract

(m,ρ)-quasi-Einstein N(κ)-contact metric manifolds have been studied and it is established that if such a manifold is a (m,ρ)-quasi-Einstein manifold, then the manifold is a manifold of constant sectional curvature κ. Further analysis has been done for gradient Einstein soliton, in particular. Obtained results are supported by an illustrative example.