AdS 3-manifolds and Higgs bundles

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  • Daniele Alessandrini
  • ,
  • Qiongling Li
In this paper we investigate the relationships between closed AdS $3$-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 Poincar\'e disc into the Grassmannian of time-like 2-planes of $R^{2,2}$.
Original languageEnglish
JournalProceedings of the American Mathematical Society
Pages (from-to)845-860
Publication statusPublished - Feb 2018

Bibliographical note

14 pages, comments are welcome

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