Sasakian Finsler manifolds

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

In this study, almost contact Finsler structures on vector bundle are defined and the condition of normality in terms of the Nijenhuis torsion Nf of almost contact Finsler structure is obtained. It is shown that for a K-contact structure on Finsler manifold \nablaX x =-\frac{1}{2} f X and the flag curvature for plane sections containing x 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.

Anahtar Kelimeler:

Finsler connection, vector bundle, almost contact manifold, Sasakian manifold, nonlinear connection, Ricci tensor

Sasakian Finsler manifolds

Keywords:

Finsler connection, vector bundle, almost contact manifold, Sasakian manifold, nonlinear connection, Ricci tensor,

PDF

___

Antonelli, P. L.: Handbook of Finsler Geometry, Volume 1, Kluver Academic Publishers, ISBN-10:1402015550, (2003).
Atanasiv, G. H., Sinha, B. B., Singh, S. K.: On Finsler spaces.3, Proc. Nat. Semi., 29–36, (1984). Miron, R.: On Finsler spaces, Proc. Nat. Semi. 2-Brasov, 147–188, (1982).
Sinha, B. B., Yadav, R. K.: On almost contact Finsler structures on vector bundle, Indian J. Pure Appl. Math, 19(1), 27–35, (1988).
Sinha, B. B., Yadav, R. K.: Almost contact semi symmetric metric Finsler connections on vector bundle, Indian J. Pure Appl. Math., 22(1), 29–39, (1991).
Szilasi, J., Vincze, C.: A new look at Finsler connections and special Finsler manifolds, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis, 16, 33–63, (2000).