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

Esmaeil Peyghan, and Chunping Zhong. "A framed f-structure on the tangent bundle of a Finsler manifold." Annales Polonici Mathematici 104.1 (2012): 23-41. <http://eudml.org/doc/286136>.

@article{EsmaeilPeyghan2012,
abstract = {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 $ = 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(·,·) = 0 iff (M,F) is a locally flat Riemannian manifold.},
author = {Esmaeil Peyghan, Chunping Zhong},
journal = {Annales Polonici Mathematici},
keywords = {framed -structure; almost contact structure; indicatrix bundle; Sasakian structure; curvature operator; local flatness},
language = {eng},
number = {1},
pages = {23-41},
title = {A framed f-structure on the tangent bundle of a Finsler manifold},
url = {http://eudml.org/doc/286136},
volume = {104},
year = {2012},
}

TY - JOUR
AU - Esmaeil Peyghan
AU - Chunping Zhong
TI - A framed f-structure on the tangent bundle of a Finsler manifold
JO - Annales Polonici Mathematici
PY - 2012
VL - 104
IS - 1
SP - 23
EP - 41
AB - 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 $ = 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(·,·) = 0 iff (M,F) is a locally flat Riemannian manifold.
LA - eng
KW - framed -structure; almost contact structure; indicatrix bundle; Sasakian structure; curvature operator; local flatness
UR - http://eudml.org/doc/286136
ER -