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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2012 | 104 | 1 | 23-41

## A framed f-structure on the tangent bundle of a Finsler manifold

EN

### Abstrakty

EN
Let (M,F) be a Finsler manifold, that is, M is a smooth manifold endowed with a Finsler metric F. In this paper, we introduce on the slit tangent bundle $\widetilde{TM}$ a Riemannian metric G̃ which is naturally induced by F, and a family of framed f-structures which are parameterized by a real parameter c≠ 0. We prove that (i) the parameterized framed f-structure reduces to an almost contact structure on IM; (ii) the almost contact structure on IM is a Sasakian structure iff (M,F) is of constant flag curvature K = c; (iii) if $𝓢 = y^{i}δ_{i}$ is the geodesic spray of F and R(·,·) the curvature operator of the Sasaki-Finsler metric which is induced by F, then R(·,·)𝓢 = 0 iff (M,F) is a locally flat Riemannian manifold.

23-41

wydano
2012

### Twórcy

autor
• Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran
autor
• School of Mathematical Sciences, Xiamen University, Xiamen 361005, China