η-Ricci solitons on para-Kenmotsu manifolds

2014/02/02 by Blaga, Adara M.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.0223

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,⋅)_W2⋅ S=0 and (ξ,⋅)_S⋅ W₂=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.

Related

• η-Ricci solitons in (ε)-almost paracontact metric manifolds
• Almost η-Ricci solitons on Kenmotsu manifolds
• η-Ricci solitons on contact pseudo-metric manifolds
• Para-Sasakian manifolds and *-Ricci solitons
• *-Conformal η-Ricci soliton within the framework of Kenmotsu manifolds