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

Abbassi, Mohamed Tahar Kadaoui; Amri, Noura

doi:10.21136/cmj.2020.0193-19

Czech.Math.J. 2020

DOI: 10.21136/cmj.2020.0193-19

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

Mohamed Tahar Kadaoui Abbassi¹,

Noura Amri²

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz

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2021

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Natural Ricci Solitons on Tangent and Unit Tangent Bundles

Abbassi¹,

Amri²

2021

Z. mat. fiz. anal. geom.

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Considering pseudo-Riemannian g-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure on the base manifold. Restricting ourselves to some class of pseudo-Riemannian g-natural metrics, we show that the tangent bundle is a Ricci soliton if and only if the base manifold is flat and the potential vector field is a complete lift of a conformal vector field. We give then a classification of conformal vector fields on the tangent bundle of a flat Riemannian manifold equipped with these g-natural metrics. When unit tangent bundles over a constant curvature Riemannian manifold are endowed with pseudo-Riemannian Kaluza-Klein type metric, we give a classification of Ricci soliton structures whose potential vector fields are fiber-preserving, inferring the existence of some of them which are non Einstein.

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Natural Ricci Solitons on Tangent and Unit Tangent Bundles

Abbassi¹,

Amri²

2021

Z. mat. fiz. anal. geom.

Self Cite

View full text Add to dashboard Cite

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

Cited by 1 publication

References 30 publications

Natural Ricci Solitons on Tangent and Unit Tangent Bundles

Natural Ricci Solitons on Tangent and Unit Tangent Bundles

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