Sasakian Finsler manifolds

Yaliniz A. F., ÇAlişKan N.

Turkish Journal of Mathematics, vol.37, no.2, pp.319-339, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1006-371
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.319-339
  • Keywords: Almost contact manifold, Finsler connection, Nonlinear connection, Riccitensor, Sasakian manifold, Vector bundle
  • Uşak University Affiliated: No

Abstract

In this study, almost contact Finsler structures on vector bundle are defined and the condition of normality in terms of the Nijenhuis torsion NΦ of almost contact Finsler structure is obtained. It is shown that for a K-contact structure on Finsler manifold ∇xΞ = 1/2ΦX and the flag curvature for plane sections containing Ξ are equal to 1/4 . By using the Sasakian Finsler structure, the curvatures of a Finsler connection ∇ on V are obtained. We prove that a locally symmetric Finsler manifold with K-contact Finsler structure has a constant curvature 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. © TÜBİTAK.