Recurrent and $\phi$-recurrent curvature on mixed 3-Sasakian manifolds

Mohammad Bagher Kazemi Balgeshir  ; Fatemeh Raei

Novi Sad Journal of Mathematics, Tome 53 (2023) no. 2.

Résumé

In this paper we study the equation $\phi_i^2(\nabla R)=A_iR$ on a mixed 3-structure manifold $(M,\xi_i,\eta_i,\phi_i,g)_{i\in \{1,2,3\}}$, where $\nabla R$ is the covariant 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 $\nabla R=A_iR$. That means that the manifold is curvature recurrent. Moreover, we prove that on a mixed 3-Sasakian manifold that equation implies $\nabla R=0$.

Détail

Publié le : 2023-01-21

DOI : 10.30755/NSJOM.10764

Classification : 53C50, 53C15
Keywords: mixed 3-structure, $\phi$-recurrent manifold, Einstein manifold, locally symmetric