Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606453 | Differential Geometry and its Applications | 2010 | 22 Pages |
Abstract
Given a principal bundle GâªPâB (each being compact, connected and oriented) and a G-invariant metric hP on P which induces a volume form μP, we consider the group of all unimodular automorphisms SAut(P,μP):={ÏâDiff(P)|ÏâμP=μP andÏ is G-equivariant} of P, and determines its Euler equation à la Arnold. The resulting equations turn out to be (a particular case of) the Euler-Yang-Mills equations of an incompressible classical charged ideal fluid moving on B. It is also shown that the group SAut(P,μP) is an extension of a certain volume preserving diffeomorphisms group of B by the gauge group Gau(P) of P.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mathieu Molitor,