Polarized harmonic mappings and optimal moving frames

Serge Preston, Robert Thompson

Abstract


We introduce the notion of a polarized harmonic mapping MN 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 MG, 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.

Keywords


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

Full Text:

PDF


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

Copyright (c) 2019 Robert Thompson

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.