Finsler geometry and natural foliations on the tangent bundle

Bejancu, Aurel; Farran, Hani Reda

doi:10.1016/s0034-4877(06)80044-3

Cited by 24 publications

(37 citation statements)

References 3 publications

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“…For the geodesic spray of a Finsler function, it is known that one can always construct an integrable distribution, transverse to the Liouville vector field, that is tangent to the indicatrix of the Finsler function [2]. In dimension 2, our Theorems 4.1 and 4.2 provide a characterization of the Finsler metrizability in terms of the integrability of such a distribution.…”

Section: Introductionmentioning

confidence: 95%

Frobenius integrability and Finsler metrizability for 2-dimensional sprays

Bucataru

Creţu

Taha

2018

Differential Geometry and its Applications

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Abstract. For a 2-dimensional non-flat spray we associate a Berwald frame and a 3-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of the given spray. In the integrable case, the sought after Finsler function is provided by a closed, homogeneous 1-form from the annihilator of the Berwald distribution. We discuss both the degenerate and non-degenerate cases using the fact that the regularity of the Finsler function is encoded into a regularity condition of a 2-form, canonically associated to the given spray. The integrability of the Berwald distribution and the regularity of the 2-form have simple and useful expressions in terms of the Berwald frame.

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Section: Introductionmentioning

confidence: 95%

Frobenius integrability and Finsler metrizability for 2-dimensional sprays

Bucataru

Creţu

Taha

2018

Differential Geometry and its Applications

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“…F is said to be of constant flag curvature [6]. It is known that a Finsler manifold (M, F ) is of constant curvature λ if and only if we have R ij = λF 2 h ij , where R ij = g ik R k j , h ij = g ij − l i l j and l i = y i F [2]. By using (1), (2) and Koszol formula, we obtain the following:…”

Section: Horizontal Liouville Vector Field With Respect To Sasaki Metricmentioning

confidence: 99%

Killing vector fields of horizontal Liouville type

Peyghan

Tayebi

2011

Comptes Rendus. Mathématique

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“…The study of interrelations between the geometry of some natural foliations on the tangent manifold of a Finsler space and the geometry of the Finsler space itself was initiated and intensively studied by Bejancu and Farran [7]. The main idea of their paper is to emphasize the importance of some foliations which exist on the tangent bundle of a Finsler space (M, F ), in studying the differential geometry of (M, F ) itself.…”

Section: 1 Introductionmentioning

confidence: 99%

A vertical Liouville subfoliation on the cotangent bundle of a Cartan space and some related structures

Ida

Manea

2014

Int. J. Geom. Methods Mod. Phys.

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In this paper we study some problems related to a vertical Liouville distribution (called vertical Liouville-Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vrȃnceanu type on Cartan spaces related to some foliated structures. Also, we identify a certain (n, 2n − 1)codimensional subfoliation (F V , F C * ) on T * M 0 given by vertical foliation F V and the line foliation F C * spanned by the vertical Liouville-Hamilton vector field C * and we give a triplet of basic connections adapted to this subfoliation. Finally, using the vertical Liouville foliation F V C * and the natural almost complex structure on T * M 0 we study some aspects concerning the cohomology of c-indicatrix cotangent bundle.

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Finsler geometry and natural foliations on the tangent bundle

Cited by 24 publications

References 3 publications

Frobenius integrability and Finsler metrizability for 2-dimensional sprays

Frobenius integrability and Finsler metrizability for 2-dimensional sprays

Killing vector fields of horizontal Liouville type

A vertical Liouville subfoliation on the cotangent bundle of a Cartan space and some related structures

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