A duality theorem for harmonic maps into inner symmetric spaces

2019/03/03 by Josef F. Dorfmeister, Peng Wang, Dorfmeister, Josef F. +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1903.00885

openalex publication_date 2019/03/03 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the loop group formalism). Locally also the inverse/converse duality theorem holds.

Related

• Introduction to Duality
• Algebraic Harmonic Maps, Totally Symmetric Harmonic Maps and a Conjecture
• Harmonic maps of finite uniton type into inner symmetric spaces
• Harmonic maps of finite uniton number into inner symmetric spaces via based normalized extended frames
• Harmonic, Holomorphic and Rational Maps from Self-Duality