Geometry, Topology and Dynamics Seminar
Ana Rechtman
UIC-CONACYT
Existence of periodic orbits of geodesible vector fields on 3-manifolds
Abstract: A vector field on a closed manifold $M$ is geodesible if there is a Riemannian metric making its orbits geodesics. After discussing some examples of geodesible vector fields and results on
the existence of periodic orbits for vector fields on closed 3-manifolds, I will sketch the proof of the existence of a periodic orbit when $M$ is either diffeomorphic to
the three sphere or has non trivial $\pi_2$ and $X$ is either: real analytic, or $C^\infty$ and preserves a volume.
On 3-manifolds, the class of geodesible vector fields contains Reeb vector fields, defined by a contact form, and vector fields that admit a
global cross section.
Monday April 19, 2010 at 3:00 PM in SEO 612