Generalized $k$-contact structures

TL;DR

This paper introduces generalized $k$-contact structures as higher codimensional analogues of contact distributions, linking them to algebraic Anosov actions and demonstrating their existence and compatibility with certain dynamical systems.

Contribution

It develops the theory of generalized $k$-contact structures and establishes their connection with algebraic Anosov actions, expanding the understanding of contact-like structures in higher dimensions.

Findings

Existence of an associated $ ext{R}^k$-action for generalized $k$-contact structures

Relation between generalized $k$-contact structures and Weyl chamber actions

Proof that certain algebraic Anosov actions admit compatible generalized $k$-contact structures

Abstract

With the goal to study and better understand algebraic Anosov actions of $\mathbb R^k$, we develop a higher codimensional analogue of the contact distribution on odd dimensional manifolds, call such structure a generalized $k$-contact structure. We show that there exist an $\mathbb R^k$-action associated with this structure, afterwards, we relate this structure with the Weyl chamber actions and a few more general algebraic Anosov actions, proving that such actions admits a compatible generalized $k$-contact structure.