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

• Autorzy: Esmaeil Peyghan , Chunping Zhong
• Języki publikacji: 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.

Kategorie tematyczne

• 53B40: Finsler spaces and generalizations (areal metrics)
• 53C60: Finsler spaces and generalizations (areal metrics)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2012
• Tom: 104
• Numer: 1
• Strony: 23-41

Daty

wydano

2012

Twórcy

autor

Esmaeil Peyghan

• Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran

autor

Chunping Zhong

• School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

Identyfikatory

DOI

10.4064/ap104-1-3