Explicit construction of harmonic two-spheres into the complex Grassmannian

2010/07/23 by Maria João Ferreira, Maria Joao Ferreira, Ferreira, Maria Joao +3 · 1 citation
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1007.4143

arxiv created 2010/07/23 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an explicit description of all harmonic maps of finite uniton number from a Riemann surface into a complex Grassmannian. Namely, starting from a constant map Q and a collection of meromorphic functions and their derivatives, we show how to algebraically construct all harmonic maps from the two-sphere into a given Grassmannian G_p(\mathbb Cⁿ). In this setting the uniton number depends on Q and p and we obtain a sharp estimate for it.

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