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arXiv · 1206.1218

Quantitative Darboux theorems in contact geometry

John B. Etnyre·Rafal Komendarczyk·Patrick Massot
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Abstract

This paper begins the study of relations between Riemannian geometry and contact topology in any dimension and continues this study in dimension 3. Specifically we provide a lower bound for the radius of a geodesic ball in a contact manifold that can be embedded in the standard contact structure on Euclidean space, that is on the size of a Darboux ball. The bound is established with respect to a Riemannian metric compatible with an associated contact form. In dimension three, it further leads us to an estimate of the size for a standard neighborhood of a closed Reeb orbit. The main tools are classical comparison theorems in Riemannian geometry. In the same context, we also use holomorphic curves techniques to provide a lower bound for the radius of a PS-tight ball.

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John B. Etnyre, Rafal Komendarczyk, Patrick Massot. 2016-02-04. Quantitative Darboux theorems in contact geometry. https://doi.org/10.1090/tran%2F6821

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