标题： 施泰纳和管公式在三维接触子黎曼几何中 显示英文标题

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

摘要： 我们证明了一个Steiner公式，适用于三维接触子黎曼流形中没有特征点的规则曲面，并且该流形配备了一个任意光滑体积。 我们得到的公式等价于一个半管公式，具有局部性质。 因此可以应用于不包含特征点区域中的任何曲面。 我们提供了展开式中出现的系数的几何解释，并在三维子黎曼模型空间的一些相关例子中计算了它们。 这些结果推广了在10.1016/j.na.2015.05.006和arXiv:1703.01592v3中针对Heisenberg群获得的结果。 显示英文摘要

摘要： 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.