Classes of Noncontact Mappings of Carnot Groups and Metric Properties

We study the metric properties of level surfacesfor classes of smooth noncontact mappingsfrom arbitrary Carnot groups into two-step oneswith some constraints on the dimensions of horizontal subbundlesand the subbundles corresponding to degree 2 fields.We calculate the Hausdorff dimension of the level surfaceswith respect to the sub-Riemannian quasimetricand derive an analytical relation between the Hausdorff measuresfor the sub-Riemannian quasimetric and the Riemannian metric.As application,we establish a new form of coarea formula, also proving thatthe new coarea factor is well defined.