三维接触亚黎曼几何中的Steiner和tube公式

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-02-02 DOI:10.1142/S0219199723500347

D. Barilari, Tania Bossio

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引用次数: 0

摘要

我们证明了具有任意光滑体积的三维接触亚黎曼流形中无特征点正则曲面的一个Steiner公式。我们得到的公式，相当于半管公式，是局部性质的。因此，它可以应用于不包含特征点的区域中的任何表面。我们给出了展开式中出现的系数的几何解释，并在三维亚黎曼模型空间的一些相关例子上计算了它们。这些结果推广了10.1016/j.na.2015.05.006和arXiv:1703.01592v3中Heisenberg组的结果。

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

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.