# Compact surfaces with no Bonnet mate

## TL;DR

This paper identifies conditions under which compact surfaces do not have Bonnet mates, focusing on isothermic and totally nonisothermic immersions, contributing to the understanding of surface rigidity.

## Contribution

It provides new sufficient conditions for the absence of Bonnet mates in compact surface immersions, expanding the classification of surface rigidity.

## Key findings

- Isothermic surfaces can have Bonnet mates under certain conditions.
- Totally nonisothermic surfaces lack Bonnet mates.
- Sufficient conditions for non-existence of Bonnet mates are established.

## Abstract

This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.