Sasakian Finsler manifolds

Abstract

In this study, almost contact Finsler structures on vector bundle are defined and the condition of normality in terms of the Nijenhuis torsion N_{\phi} of almost contact Finsler structure is obtained. It is shown that for a K-contact structure on Finsler manifold \nabla_X \xi =-\frac{1}{2} \phi X and the flag curvature for plane sections containing \xi are equal to \frac{1}{4}. By using the Sasakian Finsler structure, the curvatures of a Finsler connection \nabla on V are obtained. We prove that a locally symmetric Finsler manifold with K-contact Finsler structure has a constant curvature \frac{1}{4}. Also, the Ricci curvature on Finsler manifold with K-contact Finsler structure is given. As a result, Sasakian structures in Riemann geometry and Finsler condition are generalized. As a conclusion we can state that Riemannian Sasakian structures are compared to Sasakian Finsler structures and it is proven that they are adaptable.