Anosov actions of (n-1)-dimensional Lie groups on n-dimensional manifolds

TL;DR

This paper proves that (n-1)-dimensional unimodular Lie groups cannot act Anosovly on closed n-dimensional manifolds, establishing a non-existence result in the field of dynamical systems.

Contribution

It provides a new non-existence theorem for Anosov actions of specific Lie groups on manifolds, expanding understanding of group actions in dynamical systems.

Findings

No Anosov actions by (n-1)-dimensional unimodular Lie groups on closed n-manifolds.

Establishes constraints on possible group actions in dynamical systems.

Advances the classification of Lie group actions on manifolds.

Abstract

We show that there are no Anosov actions by (n-1)-dimensional unimodular Lie groups on closed n-dimensional manifolds.