The moduli spaces of equivariant minimal surfaces in $\RH^3$ and $\RH^4$ via Higgs bundles

TY - JOUR

T1 - The moduli spaces of equivariant minimal surfaces in $\RH^3$ and $\RH^4$ via Higgs bundles

AU - McIntosh, Ian Robert

AU - Loftin, John

N1 - © The Author(s) 2018

PY - 2018/10/9

Y1 - 2018/10/9

N2 - In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincar\'e 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 studythis moduli space for the non-compact symmetric space $\RH^n$ and show how $SO_0(n,1)$-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 $\RH^3$ and $\RH^4$, and relate their structure to the structure of the corresponding Higgs bundle moduli spaces.

AB - In this article we introduce a definition for the moduli space of equivariant minimal immersions of the Poincar\'e 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 studythis moduli space for the non-compact symmetric space $\RH^n$ and show how $SO_0(n,1)$-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 $\RH^3$ and $\RH^4$, and relate their structure to the structure of the corresponding Higgs bundle moduli spaces.

M3 - Article

SN - 1572-9168

JO - Geometriae Dedicata

JF - Geometriae Dedicata

ER -