Bi-contact structures with symmetry: local normal forms

Key Points

Local normal forms reveal the presence of symmetries in transverse contact distributions.
The approach highlights properties of orientable Anosov flows associated with contact distributions.
The findings suggest that maximal symmetries can exist at any point within specific pairs of contact distributions.
This analysis enhances our understanding of geometrical structures in 3-manifolds.

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.

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Cite This Study

Connor Jackman (Fri,) studied this question.

synapsesocial.com/papers/68e2537cd6d66a53c24746c3 https://doi.org/https://doi.org/10.48550/arxiv.2508.00802

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