# On equivalence of third order linear differential operators on two-dimensional manifolds

## TL;DR

This paper investigates the differential invariants of third order linear differential operators on two-dimensional manifolds to determine conditions for their equivalence under automorphism groups.

## Contribution

It introduces new criteria based on differential invariants for the equivalence of third order linear differential operators on 2D manifolds.

## Key findings

- Derived explicit conditions for operator equivalence
- Identified key differential invariants for classification
- Provided a framework for analyzing operator transformations

## Abstract

We study differential invariants of the third order linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles on two dimensional manifolds with respect to groups of authomorphisms.