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arXiv · 2504.06085

On the tightness of left-invariant contact structures

Eugenio Bellini
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Abstract

We prove that all left-invariant contact structures on three-dimensional Lie groups are tight. The argument is based on Riemannian methods and establishes a unique factorization property for any Lie group admitting a left-invariant contact structure, other than SU(2). We then make use of such factorization property to construct embeddings of left-invariant contact structures into the standard contact structure on $\mathbb R^3$.

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Eugenio Bellini. 2026-05-04. On the tightness of left-invariant contact structures. https://arxiv.org/abs/2504.06085

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