Geometry of Mus-Sasaki metric

Zagane, Abderrahim; Djaa, Mustapha

doi:10.2478/cm-2018-0008

Cited by 10 publications

(7 citation statements)

References 13 publications

(14 reference statements)

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“…Moreover, many metrics on tangent bundles have been introduced by deforming these two metrics. The rescaled Sasaki metric [3], the twisted Sasaki metric [4], the Mus-Sasaki metric [5], the rescaled Cheeger-Gromoll metric [6], the generalized Cheeger-Gromoll metric [7], and the Cheeger-Gromoll type metric [8] are examples of these deformations. Moreover, Latti and Djaa [9] introduced a new deformation of the Cheeger-Gromoll metric g, called the Mus-Cheeger-Gromoll metric.…”

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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Section: Introductionmentioning

confidence: 99%

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

Altunbaş

2023

Journal of New Theory

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“…The geometry of the tangent bundle T M equipped withe Sasaki metric has been studied by many authors Sasaki [24], K.Yano and S. Ishihara [26], P.Dombrowski [9], A. A. Salimov, and Gezer [12], [21], [20], [22] and others (see [1], [7], [13], [17], [25], [27]).…”

Section: Introductionmentioning

confidence: 99%

Proper biharmonic maps on tangent bundle

Djaa¹,

Latti²,

Zagane³

2022

Communications in Mathematics

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“…Musso, E., Tricerri, F. [16] has introced the notion of Cheeger-Gromoll metric, this metric has been studied also by many authors (see [1,11,21,19]). There are other metrics on the tangent bundle that is studied and published in articles (see for example [2,22].…”

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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Geometry of Mus-Sasaki metric

Abstract: In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M as a new natural metric non-rigid on T M. First we investigate the geometry of the Mus-Sasakian metrics and we characterize the sectional curvature and the scalar curvature.

Cited by 10 publications

References 13 publications

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

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

Proper biharmonic maps on tangent bundle

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

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