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math.DG2024
Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry
Aleš Návrat, Lenka Zalabová
This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+…
math.DG2016
Nilpotent approximation of a trident snake robot controlling distribution
Jaroslav Hrdina, Ales Navrat, Petr Vasik
We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with…
math.DG2014
Nonstandard operators in Grassmannian geometry
Aleš Návrat
We present a construction of curved analogues of the nonstandard operators on Grassmannians parallel to the construction of the Paneitz operator via the curved Casimir operator, bu…