Space-likeness of classes of level surfaces on Carnot groups and their metric properties

We consider $C^1$-smooth vector functions defined on Carnot groups of arbitrary depth, deduce conditions for space-likeness of their level surfaces, and describe their metric properties from the viewpoint of sub-Lorentzian geometry. We prove the coarea formula as an expression of the measure of a subset of a Carnot group in terms of the sub-Lorentzian measures of its intersections with level sets of a vector function.