Geodesic
Space-likeness of classes of level surfaces on Carnot groups and their metric properties
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 38-42

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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.
Keywords: Carnot group, sub-Lorentzian structure, vector function, level set, sub-Lorentzian measure, coarea formula. 
@article{DANMA_2020_492_a7,
     author = {M. B. Karmanova},
     title = {Space-likeness of classes of level surfaces on {Carnot} groups and their metric properties},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--42},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/}
}
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M. B. Karmanova. Space-likeness of classes of level surfaces on Carnot groups and their metric properties. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 38-42. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/