Recurrent and ϕ-recurrent curvature on mixed 3-Sasakian manifolds

چکیده مقاله

In this paper we study the equation ϕ²i (∇R) = A_iR on a mixed 3-structure manifold (M, ξ_i, η_i, ϕ_i, g)_i∈{1,2,3}, where ∇R is the co-variant derivative of the curvature tensor and A_i’s are some 1-forms. We give some examples of such manifolds and show that this equation leads to the important equation ∇R = A_iR. That means that the manifold is curvature recurrent. Moreover, we prove that on a mixed 3-Sasakian manifold that equation implies ∇R = 0. © 2023, Institute of Mathematics. All rights reserved.