Geometry of Twisted Sasaki Metric

Belarbi, Lakehal; Elhendi, Hichem

doi:10.7546/jgsp-53-2019-1-19

Cited by 4 publications

(3 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to [4], we have Remark 3.1. Let (M, g) be a Riemannian manifold, let ∇ be the Levi-Civita connection of g and let (T M, G f,h ) be it's tangent bundle equipped with the twisted Sasaki metric.…”

Section: Geometry Of Tangent Bundle With Twisted Sasaki Metricmentioning

confidence: 93%

On the geometry of lift metrics and lift connections on the tangent bundle

Peyghan¹,

Seifipour²,

Blaga³

2021

Preprint

View full text Add to dashboard Cite

show abstract

Section: Geometry Of Tangent Bundle With Twisted Sasaki Metricmentioning

confidence: 93%

On the geometry of lift metrics and lift connections on the tangent bundle

Peyghan¹,

Seifipour²,

Blaga³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…A more general metric is given by M. Anastasiei in Ref. [18] which generalizes both of the two metrics mentioned above in the following sense: it preserves the orthogonality of the two distributions, on the horizontal distribution it is the same as on the base manifold, and finally the Sasaki and the Cheeger-Gromoll metric can be obtained as particular cases of this metric. A compatible almost complex structure is also introduced and hence TM becomes a locally conformal almost Käherian manifold.…”

Section: Introductionmentioning

confidence: 99%

On the geometry of the tangent bundle with gradient Sasaki metric

Belarbi

Elhendi

2021

AJMS

Self Cite

View full text Add to dashboard Cite

PurposeLet (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature, scalar and sectional curvatures.Design/methodology/approachIn this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.FindingsThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.Originality/valueThe authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature scalar and sectional curvatures.

show abstract

Geometry of Twisted Sasaki Metric

Cited by 4 publications

References 0 publications

On the geometry of lift metrics and lift connections on the tangent bundle

On the geometry of lift metrics and lift connections on the tangent bundle

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

On the geometry of the tangent bundle with gradient Sasaki metric

Contact Info

Product

Resources

About