Cyclic surfaces and Hitchin components in rank 2

2014/06/18 by Labourie, François · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1406.4637

Abstract

We prove that given a Hitchin representation in a real split rank 2 group \mathsf G₀, 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 Hermitian bundle over Teichmüller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of \mathsf G₀. Some partial extensions of the construction hold for cyclic bundles in higher rank.

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• Equiaffine immersions and pseudo-Riemannian space forms
• Expanding Ricci solitons and Higgs bundles

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