A Lipschitz curve in the free 3-step Carnot group with 2 generators is purely unrectifiable by C^1 horizontal curves.
M´ etriques de Carnot-Carath´ eodory et quasiisom´ etries des espaces sym´ etriques de rang un
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A Lipschitz curve in a Carnot group that is purely unrectifiable by smooth horizontal curves
A Lipschitz curve in the free 3-step Carnot group with 2 generators is purely unrectifiable by C^1 horizontal curves.