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

Consider TM as the tangent bundle of a (pseudo-)Riemannian manifold M , equipped with a Ricci quarter-symmetric metric connection del. 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 phi e(Ric) vector fields within the framework of del on TM (center dot) . 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 del.

Journal

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY

Year

2024

Volume

17

Issue

2

Pages

358-377

ISSN

1307-5624

DOI

10.36890/IEJG.1352531

WoS UID

WOS:001360522200001