Polarized harmonic mappings and optimal moving frames
Serge Preston, Robert Thompson
Atti della Accademia Peloritana dei Pericolanti: Classe di Scienze Fisiche, Matematiche e Naturali · 2019
doi:10.1478/aapp.97s1a23 (opens in a new tab)
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Abstract
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 Kahler 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.
Abstract licence: CC BY
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