On integrable natural Hamiltonian systems on the suspensions of toric automorphism

TL;DR

This paper corrects a mistake in a previous work on integrable natural Hamiltonian systems on suspensions of toric automorphisms, providing a revised and accurate statement.

Contribution

It identifies an error in earlier research and offers a corrected theorem with proof regarding integrable Hamiltonian systems on specific geometric structures.

Findings

Corrected the main statement of liu

Provided a valid proof for the revised statement

Clarified the conditions for integrability in the studied systems

Abstract

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.