Accepted Paper

Inserted: 3 feb 2023
Last Updated: 1 jun 2023

Journal: Communication in Contemporary Mathematics
Year: 2023

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 previously obtained for the Heisenberg group.