Conformal Vector Fields of a Class of Finsler Spaces II

TL;DR

This paper characterizes conformal vector fields in $(eta)$-spaces, especially $(eta)$-spaces with curvature conditions, and constructs examples of non-homothetic conformal fields in Randers spaces.

Contribution

It introduces two fundamental principles for analyzing conformal vector fields in $(eta)$-spaces and applies them to specific classes, including constructing non-homothetic examples.

Findings

Conformal vector fields are homothetic under certain conditions.

Established local structure of homothetic fields in $(eta)$-spaces.

Constructed non-homothetic conformal vector fields in Randers spaces.

Abstract

In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(\alpha,\beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of some classes of $(\alpha,\beta)$ spaces under certain curvature conditions. Besides, we construct a family of non-homothetic conformal vector fields on a family of locally projectively Randers spaces.