Three dimensional f-Kenmotsu manifold satisfying certain curvature conditions

Abstract

The purpose of the present paper is to study pseudosymmetry conditions on f-Kenmotsu manifolds. RESUMENEl propósito del presente artículo es estudiar condiciones de pseudosimetría en variedades f-Kenmotsu.

On Three Dimensional Pseudosymmetric Alpha-Kenmotsu Manifolds

“…It is important to say that the condition ∧ = 0 satisfies for dimension is greater and equal than 5. This condition does not hold for the three dimensional case [15]. Accordingly, since the conformal curvature tensor in the three dimensional space will be identical to zero, we can also make the Riemannian curvature tensor calculations on the conformal curvature tensor.…”

“…In other words, we have So we can give the following results for the three dimensional case: where is a strictly positive function such that ∧ = 0. Moreover, , , and are the Riemannian curvature tensor, the Ricci tensor, the Ricci operator and the scalar curvature, respectively [15]. Proof Suppose that 3 is an alpha-Kenmotsu manifold and is a real constant.…”

“…for any vector fields , on ²ⁿ⁺¹ where α is a smooth function such that ∧ = 0. In these formulas, is the Levi-Civita connection and the Riemannian curvature tensor of ²ⁿ⁺¹ [12,13,15].…”

“…Semisymmetric Kenmotsu and alpha-Kenmotsu manifolds are studied in [8,13]. Also, the other semi symmetric conditions are investigated in [11,15] on such manifolds. In this paper, we study pseudosymmetric conditions on alpha-Kenmotsu manifolds with dimension 3.…”