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

100%

Peyghan E., Zhong C.

Annales Polonici Mathematici

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2012

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tom 104

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nr 1

23-41

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.

2

On the geometry of tangent bundles with a class of metrics

81%

Peyghan E., Heydari A., Nourmohammadi Far L.

Annales Polonici Mathematici

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2012

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tom 103

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nr 3

229-246

EN

We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.

3

Doubly warped product Finsler manifolds with some non-Riemannian curvature properties

81%

Peyghan E., Tayebi A., Najafi B.

Annales Polonici Mathematici

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2012

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tom 105

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nr 3

293-311

EN

We consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian if and only if it is Berwaldian. Then we prove that every relatively isotropic Landsberg DWP-manifold is a Landsberg manifold. We show that a relatively isotropic mean Landsberg warped product manifold is a weakly Landsberg manifold. Finally, we show that there is no locally dually flat proper DWP-Finsler manifold.

Ograniczanie wyników

3 Annales Polonici Mathematici

3 Peyghan E.

1 Heydari A.

1 Najafi B.

1 Nourmohammadi Far L.

1 Tayebi A.

1 Zhong C.

3 2012

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

On the geometry of tangent bundles with a class of metrics

Doubly warped product Finsler manifolds with some non-Riemannian curvature properties