ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC

Author:

PEYGHAN ESMAEIL1,TAYEBI AKBAR2

Affiliation:

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

2. Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

Abstract

In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Classification of Conformal Vector Fields on the Tangent Bundle;Ukrainian Mathematical Journal;2020-10

2. A classification of conformal vector fields on the tangent bundle;Ukrains’kyi Matematychnyi Zhurnal;2020-04-29

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