Projective Vector Fields on the Tangent Bundle with a Class of Riemannian Metrics

Gezer, Aydın; Bilen, Lokman

doi:10.7546/crabs.2018.05.01

Cited by 2 publications

(2 citation statements)

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“…Nurowski and Randall [23] introduced generalized Ricci solitons, and Kumara et al [24] demonstrated that a Riemannian concurrent-recurrent manifold is Einstein when its metric is a generalized Ricci-type soliton. Gezer, Bilen, and De [25] explored almost Ricci and almost Yamabe soliton structures on the tangent bundle using the ciconia metric. Recently, Li and Khan et al studied solitons, inequalities, and submanifolds using soliton theory, submanifold theory, and other related theories [26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Yan,

Li,

Bilen

et al. 2024

Mathematics

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Let (M,∇,g) be a statistical manifold and TM be its tangent bundle endowed with a twisted Sasaki metric G. This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle TM. The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle TM according to the twisted Sasaki metric G.

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Section: Introductionmentioning

confidence: 99%

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Yan,

Li,

Bilen

et al. 2024

Mathematics

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“…In [4], fiber-preserving projective vector fields with respect to the Levi-Civita connection from this subclass of g-natural metric are considered. It is proved that the Theorem A is true about of this class of metrics.…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics

Zohrehvand¹

2020

International Electronic Journal of Geometry

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Let (M, g) be a Riemannian manifold and T M be its tangent bundle. In the present paper, we study infinitesimal projective transformations on T M with respect to the Levi-Civita connection of a class of (pseudo-)Riemannian metricsg which is a generalization of the three classical lifts of the metric g. We characterized this type of transformations and then we prove that if (T M,g) admits a non-affine infinitesimal projective transformation, then M and T M are locally flat.

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Projective Vector Fields on the Tangent Bundle with a Class of Riemannian Metrics

Cited by 2 publications

References 0 publications

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Infinitesimal Projective Transformations on the Tangent Bundle of a Riemannian Manifold with a Class of Lift Metrics

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