Harmonic vector fields on pseudo-Riemannian manifolds

Friswell, Robert; Wood, Carol

doi:10.1016/j.geomphys.2016.10.015

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2018

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Cited by 3 publications

(1 citation statement)

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“…Furthermore, we denote by X h and X v the horizontal and vertical lifts of any vector field X on M , respectively. There are many papers ( [1], [3], [5], [10], [8], [9]) which are on differential geometric structures on tangent and cotangent bundles like the Riemannian metrics, harmonic sections, almost complex structures, connections and so on.…”

Section: Introductionmentioning

confidence: 99%

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Baghban

Abedi

2018

Communications in Mathematics

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In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

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Section: Introductionmentioning

confidence: 99%

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Baghban

Abedi

2018

Communications in Mathematics

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Biharmonic vector fields on pseudo-Riemannian manifolds

Markellos

Urakawa

2018

Journal of Geometry and Physics

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Isotropic almost complex structures and harmonic unit vector fields

Baghban¹,

Abedi²

2018

Arch. Math. (Brno)

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Aguilar introduced isotropic almost complex structures J δ,σ on the tangent bundle of a Riemannian manifold (M, g). In this paper, some results will be obtained on the integrability of these structures. These structures with the Liouville 1-form define a class of Riemannian metrics g δ,σ on T M which are a generalization of the Sasaki metric. Moreover, the notion of a harmonic unit vector field is introduced with respect to these metrics like as the Sasaki metric and the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field are obtained.

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Harmonic vector fields on pseudo-Riemannian manifolds

Cited by 3 publications

References 12 publications

A new class of almost complex structures on tangent bundle of a Riemannian manifold

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Biharmonic vector fields on pseudo-Riemannian manifolds

Isotropic almost complex structures and harmonic unit vector fields

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