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Presented By: Geometry Seminar - Department of Mathematics

GEOMETRY SEMINAR: Metric Lines in Carnot groups

Alejandro Bravo Doddoli (UM)

Among nilpotent Lie groups, Carnot groups form a particularly important subclass, with the Heisenberg group being the most well-known example. Carnot groups admit the structure of a sub-Riemannian manifold. Thus, to broaden the context, a sub-Riemannian geodesic is a local arc-length-minimizing curve. A natural question is: What are the conditions for a geodesic to be a global minimizer? A curve is called a metric line if it is a globally minimizing geodesic; an alternative term is “an isometric embedding of the real line.” The talk is devoted to presenting the results and ideas that inspired me to formulate a conjecture classifying metric lines in Carnot groups, as well as the results obtained in this direction.

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