On infinitesimal conformal transformations with respect to the Cheeger-Gromoll metric

Gezer, Aydın; Bilen, Lokman

doi:10.2478/v10309-012-0009-4

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…In this context, we can find various studies focusing on conformal or Killing vector fields on some special pseudo-Riemannian manifolds. For example, in the framework of the Riemannian geometry of tangent bundles, Killing and conformal vector fields had been classified on tangent bundles of Riemannian manifolds, equipped with the Sasaki metric (see [28] and [29]) and the Cheeger-Gromoll metric (see [8] and [18]), respectively. When the tangent bundle is endowed with an arbitrary g-natural metric, it is not easy to find a full classification of conformal or Killing vector fields, but we can find some partial results on the subject (see [17] for Killing vector fields and [2], [20], [25] for conformal vector fields).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On $g$-natural conformal vector fields on unit tangent bundles

Abbassi¹,

Amri²

2020

Czech.Math.J.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On $g$-natural conformal vector fields on unit tangent bundles

Abbassi¹,

Amri²

2020

Czech.Math.J.

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“…These kinds of preserving the metric help to categorize the spaces in the sense of diffeomorphism and symmetry. The study of conformal vector fields on Riemannian manifolds and their tangent bundles is of interest to many researchers (see for instance [1,18,25,32]).…”

Section: Leila Samereh and Esmaeil Peyghanmentioning

confidence: 99%

Conformal vector fields on statistical manifolds

Samereh¹,

Peyghan²

2022

Revista De La Unión Matemática Argentina

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Introducing the conformal vector fields on a statistical manifold, we present necessary and sufficient conditions for a vector field on a statistical manifold to be conformal. After presenting some examples, we classify the conformal vector fields on two famous statistical manifolds. Considering three statistical structures on the tangent bundle of a statistical manifold, we study the conditions under which the complete and horizontal lifts of a vector field can be conformal on these structures.

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“…Killing vector field). Infinitesimal conformal transformations are studied on tangent bundles by many authors [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A Short Note on a Mus-Cheeger-Gromoll Type Metric

Altunbaş

2023

Journal of New Theory

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In this paper, we first show that the complete lift $U^{c}$ to $TM$ of a vector field $U$ on $M$ is an infinitesimal fiber-preserving conformal transformation if and only if $U$ is an infinitesimal homothetic transformation of $(M,g)$. Here, $(M, g)$ is a Riemannian manifold and $TM$ is its tangent bundle with a Mus-Cheeger-Gromoll type metric $\tilde{g}$. Secondly, we search for some conditions under which $\left(\overset{h}{\nabla},\tilde{g}\right)$ is a Codazzi pair on $TM$ when $(\nabla, g)$ is a Codazzi pair on $M$ where $\overset{h}{\nabla}$ is the horizontal lift of a linear connection $\nabla$ on $M$. We finally discuss the need for further research.

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On infinitesimal conformal transformations with respect to the Cheeger-Gromoll metric

Abstract: The present paper deals with the classification of infinitesimal fibre-preserving conformal transformations on the tangent bundle, equipped with the Cheeger-Gromoll metric

Cited by 4 publications

References 19 publications

On $g$-natural conformal vector fields on unit tangent bundles

On $g$-natural conformal vector fields on unit tangent bundles

Conformal vector fields on statistical manifolds

A Short Note on a Mus-Cheeger-Gromoll Type Metric

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