Symmetric shift-invariant subspaces and harmonic maps

2019/08/05 by Aleman, Alexandru, Pacheco, Rui, Wood, John C.
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1908.01557

Abstract

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. In particular, we obtain new general forms for such symmetric shift-invariant subspaces and for the corresponding extended solutions.

Related

• Harmonic maps and shift-invariant subspaces
• Harmonic maps into Grassmannian manifolds
• Group actions and deformations for harmonic maps
• Harmonic Riemannian submersions between Riemannian symmetric spaces of noncompact type
• Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture