CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2

François Labourie (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We prove that given a Hitchin representation in a real split rank 2 group G 0 , there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a Hermit-ian bundle over Teichmüller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of G 0. Some partial extensions of the construction hold for cyclic bundles in higher rank.

Domaines: Géométrie différentielle [math.DG]

François Labourie. CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2. Annals of Mathematics, 2017. ⟨hal-01141620⟩