Classification of Vector Fields and Soliton Structures on a Tangent Bundle with a Ricci Quarter-Symmetric Metric Connection

Year 2024, Volume: 17 Issue: 2, 358 - 377, 27.10.2024

Aydın Gezer , Erkan Karakaş

https://doi.org/10.36890/iejg.1352531

Abstract

Consider $TM$ as the tangent bundle of a (pseudo-)Riemannian manifold $M$, equipped with a Ricci quarter-symmetric metric connection $\overline{\nabla }$. This research article aims to accomplish two primary objectives. Firstly, the paper undertakes the classification of specific types of vector fields, including incompressible vector fields, harmonic vector fields, concurrent vector fields, conformal vector fields, projective vector fields, and $% \widetilde{\varphi }(Ric)$ vector fields, within the framework of $\overline{% \nabla }$ on $T\dot{M}$. Secondly, the paper establishes the necessary and sufficient conditions for the tangent bundle $TM$ to become as a Riemannian soliton and a generalized Ricci-Yamabe soliton with regard to the connection $\overline{\nabla }$.

Keywords

Complete lift metric, Ricci quarter-symmetric metric connection, tangent bundle, vector field, Riemannian soliton, generalized Ricci-Yamabe soliton

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