In the context of paracontact geometry, η-Ricci solitons are considered on manifolds satisfying certain curvature conditions: R(ξ,X) · S = 0, S · R(ξ,X) = 0, W2(ξ,X) · S = 0 and S · W2(ξ,X) = 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 R(ξ,X) · S = 0, then (M, g) is Ei...

It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2-dimensional Einstein manifold, (M, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1. Thus, (M, g) is the quotient of a space form and the metric, g, is completely determined by the ...

‎In the paper‎, ‎we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior‎. ‎Then‎, ‎their applications to optimality conditions for quasi-relative efficient solutions are obtained‎. ‎Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...