Liouville and geodesic Ricci solitons

Crâşmăreanu, Mircea

doi:10.1016/j.crma.2009.10.008

Cited by 8 publications

(5 citation statements)

References 6 publications

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“…It is well known that, on the tangent bundle TM, there exists a globally vector field S = y i δ δx i called the horizontal Liouville vector field [1], or geodesic spray [4]. We define horizontal Liouville type vector fields ξ = l i δ δx i = 1 F S and ξ = …”

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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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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“…Basic details and a collection of research papers on this area for the Riemannian case are available in [21,22], respectively. ere are few papers on Ricci solitons for semi-Riemannian (in particular, Lorentzian) manifolds (for example, see Crasmareanu [23], Brozos-Va � zquez et al [24], and Onda [25]). In year 2011, Pigola et al [26] introduced a modified concept of the Ricci solitons equation called almost Ricci solitons (briefly, ARS) by allowing the soliton constant α to be a variable function.…”

Section: Proposition 3 (See [10]) a Vector Field ξ On A Semi-riemannian Manifold (M G) Is An Acv If And Only Ifmentioning

confidence: 99%

A New Class of Contact Pseudo Framed Manifolds with Applications

Duggal

2021

International Journal of Mathematics and Mathematical Sciences

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In this paper, we introduce a new class of contact pseudo framed (CPF)-manifolds M , g , f , λ , ξ by a real tensor field f of type 1,1 , a real function λ such that f 3 = λ 2 f where ξ is its characteristic vector field. We prove in our main Theorem 2 that M admits a closed 2-form Ω if λ is constant. In 1976, Blair proved that the vector field ξ of a normal contact manifold is Killing. Contrary to this, we have shown in Theorem 2 that, in general, ξ of a normal CPF-manifold is non-Killing. We also have established a link of CPF-hypersurfaces with curvature, affine, conformal collineations symmetries, and almost Ricci soliton manifolds, supported by three applications. Contrary to the odd-dimensional contact manifolds, we construct several examples of even- and odd-dimensional semi-Riemannian and lightlike CPF-manifolds and propose two problems for further consideration.

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“…The tangent bundle equipped with the Sasaki metric has been studied by many authors among them are: Sasaki, S. [20], Crasmareanu, M. [4], Dombrowski, P. [6], Salimov, A., Gezer, A., Cengiz, N. [3,10,18] etc... The rigidity of Sasaki metric has incited some geometers to construct and study other metrics on the tangent bundle.…”

Section: Introductionmentioning

confidence: 99%

Notes About a Harmonicity on the Tangent Bundle with Vertical Rescaled Metric

Zagane

2022

International Electronic Journal of Geometry

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In this article, we present some results concerning the harmonicity on the tangent bundle equipped with the vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the vertical rescaled metric and we construct some examples of harmonic vector fields. We also study the harmonicity of a vector field along with a map between Riemannian manifolds, the target manifold is equipped with a vertical rescaled metric on its tangent bundle. Next we also discuss the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being whose tangent bundle is endowed with a vertical rescaled metric. Finally, we study the harmonicity of the tangent map also the harmonicity of the identity map of the tangent bundle.

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Liouville and geodesic Ricci solitons

Cited by 8 publications

References 6 publications

Killing vector fields of horizontal Liouville type

Killing vector fields of horizontal Liouville type

A New Class of Contact Pseudo Framed Manifolds with Applications

Notes About a Harmonicity on the Tangent Bundle with Vertical Rescaled Metric

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