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Sasakian Finsler Manifolds, Ayşe Funda Yaliniz, Nesri̇n Çalişkan

Turkish Journal of Mathematics

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 …