A Hopf-Rinow Theorem for singular Riemannian spaces

Speaker: Matias del Hoyo, UFF.

Date: 11 oct 2019, 14h.

Place: Room 407, Bloco H, Campus Gragoatá, UFF.

Abstract: Differentiable stacks include manifolds and orbifolds as particular examples, and more general singular spaces. A theory of metrics over them has been recently proposed, with emphasis in their geodesic flows. In a joint work with M. de Melo (UFSCar) we explore the Riemannian geometry of these singular spaces, and develop singular version of classic results, including a Hopf-Rinow Theorem for stacks. I will overview the basics on differentiable stacks and their metrics, present our results explaining analogies and differences with the smooth case, and relate our contributions with previous works on geodesics of orbit spaces of actions and leaf spaces of foliations.