Bi-contact structures with symmetry: local normal forms

TL;DR

This paper classifies local normal forms of bi-contact structures with symmetries on 3-manifolds, revealing that certain Anosov flows can be globally represented by intersecting contact distributions with maximal local symmetries.

Contribution

It provides the first classification of local normal forms for symmetric bi-contact structures on 3-manifolds, linking them to Anosov flows.

Findings

Orientable Anosov flows can be globally represented by intersecting contact distributions.

Local normal forms are classified for pairs of contact distributions with symmetries.

Symmetries are maximal around any point in the classified structures.

Abstract

A pair of transverse contact distributions on a 3-manifold will in general admit no 1-parameter families of symmetries: a flow preserving both contact distributions. Here, we will determine local normal forms for such pairs admitting symmetries. In particular, we observe that orientable Anosov flows may be globally given by the intersection of a pair of oppositely oriented contact distributions admitting, around any point, maximal local symmetries.