Arnol'd showed that incompressible, inviscid fluids trace out geodesics on the group of volume-preserving diffeomorphisms, and conjectured that the curvature of this group determines the stability of fluids. In this talk I will present the basic results on the curvature and a technique for obtaining explicit examples of Jacobi fields. I will also explain why these examples show that curvature cannot be used to predict stability.
Geometry-Topology Seminar
Thursday, September 26, 2002 - 4:30pm
Stephen Preston
University of Pennsylvania