Article ID Journal Published Year Pages File Type
4606453 Differential Geometry and its Applications 2010 22 Pages PDF
Abstract
Given a principal bundle G↪P→B (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):={φ∈Diff(P)|φ∗μP=μP andφ 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
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