Identity theorems for equivariant harmonic maps between spheres
Abstract
We construct moduli spaces of G-equivariant harmonic maps between spheres, where G is a subgroup of the orthogonal group. For $$G=\text {SU}(m)$$ , $$\text {U}(m)$$ , $$\text {Sp}(m)$$ , $$\text {Sp}(m)\times \text {U}(1)$$ or $$\text {Sp}(m)\times \text {Sp}(1)$$ , we obtain identity theorems: (i) The restriction to $$S^5$$ of any $$\text {SU}(m)$$ -equivariant harmonic map of $$S^{2m-1}$$ is $$\text {SU}(3)$$ -equivariant and harmonic. (ii) Any $$\text {SU}(3)$$ -equivariant harmonic map of $$S^5$$ can be uniquely extended to an $$\text {SU}(m)$$ -equivariant harmonic map of $$S^{2m-1}$$ . For the other groups, we have similar results.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Analytic and geometric function theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- manuscripta mathematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 177
- Issue
- 1
- Publication date
- 19 January 2026
- Language
- EN