Sub-Riemannian Geometry of Osculating Curves - From Tangent Lines to Algebraic Curves

Explore a 57-minute mathematical lecture that delves into nonholonomic constraints and sub-Riemannian geometry through the lens of osculating curves. Begin with the fundamental concept of tangent line movement along smooth plane curves, then advance to more complex scenarios involving osculating algebraic curves of degree N>1. Learn about vector distributions and sub-Riemannian structures derived from geometric models, with particular emphasis on osculating conics and cubics. Recorded during the "Frontiers in Sub-Riemannian Geometry" conference at the Centre International de Rencontres Mathématiques in Marseille, France, this presentation offers deep mathematical insights with chapter markers and keywords for easy navigation. Access additional resources including abstracts, bibliographies, and Mathematics Subject Classification through CIRM's Audiovisual Mathematics Library.