Séminaire de GéométrieHarmonic maps, unitons and filtrations
Martin Svensson (Odense, Danemark)
vendredi 01 juillet 2011 14:00 - Tours - Salle 2290 (Bât E2)
Harmonic maps have been intensively researched in differential geometry for several decades. Since the work of Uhlenbeck, it is known that harmonic maps from a Riemann surface into U(n) can be generated from holomorphic data by adding a uniton; when the map is of finite uniton number, this procedure gives all harmonic maps. This leads to the notion of extended solutions: holomorphic maps into loop groups satisfying a first order ordinary differential equation, thus generalizing the classical twistor constructions of Calabi. In this talk, I will discuss some different types of unitons, and show how one may produce these using the Grassmannian model of Segal. I will also discuss how one may factorize extended solutions which correspond to harmonic maps into SO(n) or Sp(n). Finally, I will give some examples of both real and symplectic harmonic maps, and their unitons.