Geometria em Lisboa

20 de Junho, 14h30

Infinitesimal Deformations of Harmonic Maps
Sala B3-01

John C. Wood (University of Leeds)

Abstract:

A harmonic map is a map between Riemannian manifolds which extremizes a natural energy functional. Its infinitesimal deformations, or Jacobi fields, are variations which preserves harmonicity to first order. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from variations through harmonic maps. If they do, then the space of harmonic maps is a smooth manifold with tangent space given by the Jacobi fields; we also gain some information on the structure of the singular set of weakly harmonic maps. We shall outline what is known about Jacobi fields and their integrability starting with closed geodesics and moving on to harmonic maps from surfaces.

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