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.

中文翻译：

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卡诺群和度量性质的非接触映射类

我们研究了从任意卡诺群到两步群的平滑非接触映射类的水平面的度量性质，并对水平子丛和对应于 2 度场的子丛的尺寸进行了一些限制。我们计算了相对于亚黎曼准度量的水平面的豪斯多夫维数，并推导了亚黎曼准度量的豪斯多夫测度与黎曼度量之间的解析关系。作为应用，我们建立了一种新形式的面积公式，也证明了新的面积因子是明确定义的。