“The symplectic reduction of sub-Riemannian geodesic flow in metabelian Carnot groups”
Giovedì 23 Marzo 2023, ore 11:00 - Aula 2BC30 - Alejandro Bravo Doddoli (University of California, Santa Cruz)
A metabelian group is a group such that [G, G] is abelian. We established a correspondence, making a symplectic reduction, between the regular geodesics in a metabelian Carnot group G and the space of solutions to a family of classical electro-mechanical systems in Euclidean space. The correspondence characterizes when these normal subRiemannian geodesic flows are integrable or admit no closed geodesics. Moreover, we can classify the integrable subRiemannian geodesic flow on the Carnot group with a rank higher than 2, which is a more general perspective than previously.