AdS 3-manifolds and Higgs bundles

Abstract

In this paper we investigate the relationships between closed AdS 3 3 -manifolds and Higgs bundles. We have a new way to construct AdS structures that allows us to see many of their properties explicitly, for example we can recover the very recent formula by Tholozan for their volume.

We give natural foliations of the AdS structure with time-like geodesic circles and we use these circles to construct equivariant minimal immersions of the Poincaré disc into the Grassmannian of time-like 2-planes of R 2 , 2 \mathbb {R}^{2,2} .