Classes of Noncontact Mappings of Carnot Groups and Metric Properties

Pub Date : 2023-11-24 DOI:10.1134/s0037446623060083
M. B. Karmanova
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Abstract

We study the metric properties of level surfaces for classes of smooth noncontact mappings from arbitrary Carnot groups into two-step ones with some constraints on the dimensions of horizontal subbundles and the subbundles corresponding to degree 2 fields. We calculate the Hausdorff dimension of the level surfaces with respect to the sub-Riemannian quasimetric and derive an analytical relation between the Hausdorff measures for the sub-Riemannian quasimetric and the Riemannian metric. As application, we establish a new form of coarea formula, also proving that the new coarea factor is well defined.

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卡诺群的非接触映射类及度量性质
研究了从任意卡诺群到两步卡诺群的光滑非接触映射类的水平曲面的度量性质,并对水平子束和对应于2次域的子束的维数进行了约束。我们计算了水平面相对于次黎曼拟度量的豪斯多夫维数,并推导了次黎曼拟度量和黎曼度量的豪斯多夫测度之间的解析关系。作为应用,我们建立了一种新的共面积公式形式,并证明了新的共面积因子是定义良好的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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