Geometry of the group Diff(S1) of diffeomorphisms of the circle. Vector fields with divergence zero on the group of diffeomorphisms of the two dimensional torus

✍ Scribed by H. Airault

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 175 KB
• Volume: 57
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200900019

✦ Synopsis

Abstract

After summarizing some results on the group of diffeomorphisms of the circle Diff(S^1^), we consider the group of diffeomorphisms of the two dimensional torus Diff(S^1^ × S^1^). We give an expression for the bracket of vector fields on this group. With the trigonometric functions sin and cos, we define a Hilbert transform on vector fields with vanishing divergence.