The moduli spaces of equivariant minimal surfaces in RH3 and RH4 via Higgs bundles

John Loftin, Ian McIntosh

Research output: Contribution to journalArticle

Abstract

In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincaré disc into a non-compact symmetric space, where the equivariance is with respect to representations of the fundamental group of a compact Riemann surface of genus at least two. We then study this moduli space for the non-compact symmetric space RHn and show how SO(n, 1) -Higgs bundles can be used to parametrise this space, making clear how the classical invariants (induced metric and second fundamental form) figure in this picture. We use this parametrisation to provide details of the moduli spaces for RH3 and RH4, and relate their structure to the structure of the corresponding Higgs bundle moduli spaces.

Original languageEnglish (US)
Pages (from-to)325-351
Number of pages27
JournalGeometriae Dedicata
Volume201
Issue number1
DOIs
StatePublished - Aug 1 2019

Fingerprint

Higgs Bundles
Minimal surface
Equivariant
Moduli Space
Symmetric Spaces
Minimal Immersion
Equivariance
Second Fundamental Form
Fundamental Group
Riemann Surface
Parametrization
Figure
Genus
Metric
Invariant

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Character variety
  • Higgs bundle
  • Minimal surface

Cite this

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The moduli spaces of equivariant minimal surfaces in RH3 and RH4 via Higgs bundles. / Loftin, John; McIntosh, Ian.

In: Geometriae Dedicata, Vol. 201, No. 1, 01.08.2019, p. 325-351.

Research output: Contribution to journalArticle

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