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 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 is the geodesic spray of F and R(·,·) the curvature operator of the Sasaki-Finsler metric which is induced by F, then R(·,·) = 0 iff (M,F) is a locally flat Riemannian manifold.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-3,
author = {Esmaeil Peyghan and Chunping Zhong},
title = {A framed f-structure on the tangent bundle of a Finsler manifold},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {23-41},
zbl = {1253.53020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-3}
}
Esmaeil Peyghan; Chunping Zhong. A framed f-structure on the tangent bundle of a Finsler manifold. Annales Polonici Mathematici, Tome 105 (2012) pp. 23-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap104-1-3/