Polarized harmonic mappings and optimal moving frames

Serge Preston, Robert Thompson


We introduce the notion of a polarized harmonic mapping M N of Riemannian manifolds and its infinitesimal analogue, a polarized harmonic connection. We study the integrability of these polarized harmonic connections when M is foliated by the action of a Lie group G.  In the case that M is a Kähler manifold and G has dimension 1, the polarized harmonic connection is integrable and we obtain a polarized harmonic mapping M G, known as an optimal moving frame (or optimal G-frame). These ideas are illustrated using the dynamical system of N-point vortices in the plane.


Dynamical systems; Lie group actions; foliations; moving frames; harmonic mappings

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DOI: http://dx.doi.org/10.1478/AAPP.97S1A23

Copyright (c) 2019 Robert Thompson

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