η-Ricci solitons on Lorentzian para-Sasakian manifolds

Abstract

In the context of paracontact geometry, η-Ricci solitons are considered on manifolds satisfying certain curvature conditions: (ξ, ·) R · S = 0, (ξ, ·) S · R = 0, (ξ, ·) W 2 · S = 0 and (ξ, ·) S · W 2 = 0. We prove that on a para-Kenmotsu manifold (M, ϕ, ξ, η, g), the existence of an η-Ricci soliton implies that (M, g) is quasi-Einstein and if the Ricci curvature satisfies (ξ, ·) R · S = 0, then (M, g) is Einstein. Conversely, we give a sufficient condition for the existence of an η-Ricci soliton on a para-Kenmotsu manifold.

η-Ricci solitons in (ε)-almost paracontact metric manifolds

“…where £ V denotes the Lie-derivative in the direction V, S stands for the Ricci tensor field, λ and µ are constants and X, Y are arbitrary vector fields on M. In [7] the authors studied η-Ricci solitons on Hopf hypersurfaces in complex space forms. In the context of paracontact geometry η-Ricci solitons were investigated in [4,5,3].…”

Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector field

“…Thereafter Ricci solitons in contact metric manifolds have been studied by various authors such as Bagewadi et. al ( [5], [6], [7], [26]), Bejan and Crasmareanu [8], Blaga [10], Chandra et. al [13], Chen and Deshmukh [14], Deshmukh et.…”

Η-Ricci SOLITONS ON 3-Dimensional N(k)-Contact METRIC MANIFOLDS

“…where S is the Ricci tensor associated to g. In this connection we mention the works of Blaga ([4], [5]) and Prakasha et. al.…”