Harmonic morphisms and the Jacobi operator
Stefano Montaldo, John C. Wood
TL;DR
This paper demonstrates that harmonic morphisms maintain the Jacobi operator along harmonic maps and uses this to establish rigidity properties of harmonic morphisms to spheres.
Contribution
It proves that harmonic morphisms preserve the Jacobi operator and applies this to show rigidity of harmonic morphisms to spheres.
Findings
Harmonic morphisms preserve the Jacobi operator along harmonic maps
Rigidity of harmonic morphisms to spheres is established
Results contribute to understanding the structure of harmonic morphisms
Abstract
We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Topological and Geometric Data Analysis · Point processes and geometric inequalities