# Classification of integrable vector equations of geometric type

## TL;DR

This paper provides a comprehensive classification of isotropic vector equations of geometric type with higher symmetries, introduces new integrable multi-component systems, and explores their auto-Bäcklund transformations.

## Contribution

It offers the first complete classification of such equations and presents novel integrable systems and their transformations.

## Key findings

- New integrable multi-component systems identified
- Complete classification of isotropic vector equations achieved
- Auto-Bäcklund transformations for these systems developed

## Abstract

A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are found.