A Note On Conformal Vector Fields Of $(\alpha,\beta)$-Spaces

TL;DR

This paper characterizes conformal vector fields in $(eta,eta)$-spaces using PDEs and explores their properties in singular cases under specific geometric conditions.

Contribution

It provides a PDE-based characterization of conformal vector fields in both regular and singular $(eta,eta)$-spaces, extending previous understanding.

Findings

Derived PDE conditions for conformal vector fields in $(eta,eta)$-spaces

Identified properties of conformal vector fields in singular $(eta,eta)$-spaces

Analyzed geometric conditions affecting conformal vector fields

Abstract

In this paper, we characterize conformal vector fields of any (regular or singular) $(\alpha,\beta)$-space with some PDEs. Further, we show some properties of conformal vector fields of a class of singular $(\alpha,\beta)$-spaces satisfying certain geometric conditions.