Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

Abbassi, Mohamed Tahar Kadaoui; Amri, Noura; Bejan, Cornelia-Livia

doi:10.1007/s00009-020-01690-5

Cited by 8 publications

(6 citation statements)

References 12 publications

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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%

“…So X reduces to a Killing vector field. Putting the second equation of (4.21) in (4.22) (i) yields 2K 1 21…”

Section: Conformal Vector Fields On Statistical Manifoldsmentioning

confidence: 99%

“…So X is a Killing vector field. Putting i = j = 1, r = 2 in (4.5) yields K 1 11 ∂ 1 (X 2 ) = 0, which gives us ∂ 1 (X 2 ) = 0. This equation together with the third equation of (4.28) results in ∂ 2 (X 1 ) = 0.…”

Section: Conformal Vector Fields On Statistical Manifoldsmentioning

confidence: 99%

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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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Section: Leila Samereh and Esmaeil Peyghanmentioning

confidence: 99%

“…So X reduces to a Killing vector field. Putting the second equation of (4.21) in (4.22) (i) yields 2K 1 21…”

Section: Conformal Vector Fields On Statistical Manifoldsmentioning

confidence: 99%

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Conformal vector fields on statistical manifolds

Samereh¹,

Peyghan²

2022

Revista De La Unión Matemática Argentina

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“…Conformal vector fields and conformal mappings play important roles in the geometry of (pseudo-)Riemannian manifolds as well as in the general relativity (see, e.g., [1][2][3][4][5]). The characterization of important spaces, such as Euclidean spaces, Euclidean spheres and hyperbolic spaces, represents one of the most fascinating problems in Riemannian geometry.…”

Section: Introductionmentioning

confidence: 99%

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

2021

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“…An interesting problem in Riemannian geometry is to find characterizations of spheres and hemispheres in the class of compact connected Riemannian manifolds with empty and non-empty boundary, respectively (see, e.g., [1,8,9,10,23,13,19,20]).…”

Section: Introductionmentioning

confidence: 99%

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold with Boundary

Freitas¹,

Evangelista²,

Viana³

2021

Preprint

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Let (M n , g) be an n-dimensional compact connected Riemannian manifold with smooth boundary. In this article, we study the effects of the presence of a nontrivial conformal vector field on (M n , g). We used the wellknown de-Rham Laplace operator and a nontrivial solution of the famous Fischer-Marsden differential equation to provide two characterizations of the hemisphere S n + (c) of constant curvature c > 0. As a consequence of the characterization using the Fischer-Marsden equation, we prove the cosmic no-hair conjecture under a given integral condition.

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Conformal Vector Fields and Ricci Soliton Structures on Natural Riemann Extensions

Cited by 8 publications

References 12 publications

Conformal vector fields on statistical manifolds

Conformal vector fields on statistical manifolds

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold with Boundary

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