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arXiv · 2302.01256

Steiner and tube formulae in 3D contact sub-Riemannian geometry

Davide Barilari·Tania Bossio
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Abstract

We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature. It can thus be applied to any surface in a region not containing characteristic points. We provide a geometrical interpretation of the coefficients appearing in the expansion, and compute them on some relevant examples in three-dimensional sub-Riemannian model spaces. These results generalize those obtained in 10.1016/j.na.2015.05.006 and arXiv:1703.01592v3 for the Heisenberg group.

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Davide Barilari, Tania Bossio. 2023-02-02. Steiner and tube formulae in 3D contact sub-Riemannian geometry. https://doi.org/10.1142/s0219199723500347

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