# Conformal deformations preserving the Finslerian $R$-Einstein criterion

## TL;DR

This paper investigates how conformal deformations can preserve the Finslerian $R$-Einstein criterion, providing a characterization of local conformal invariance between such metrics on manifolds.

## Contribution

It introduces conditions under which conformal deformations preserve the Finslerian $R$-Einstein property and characterizes local conformal invariance between these metrics.

## Key findings

- Conformal deformations preserving the $R$-Einstein criterion are explicitly described.
- A characterization of local conformal invariance between Finslerian $R$-Einstein metrics is provided.
- The results apply to $C^4$-manifolds with Finslerian metrics.

## Abstract

Given a Finslerian metric $F$ on a $C^4$-manifold, conformal deformations of $F$ preserving the $R$-Einstein criterion are presented. In particular, locally conformal invariance between two Finslerian $R$-Einstein metrics is characterized.