Research output: Chapter in Book/Report/Conference proceeding › Chapter

**Cubic Differentials in the Differential Geometry of Surfaces.** / Loftin, John; McIntosh, Ian.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Loftin, J & McIntosh, I 2015, Cubic Differentials in the Differential Geometry of Surfaces. in A Papadopoulos (ed.), *Handbook of Teichmueller Theory.* vol. V, European Mathematical Society.

Loftin, J., & McIntosh, I. (Accepted/In press). Cubic Differentials in the Differential Geometry of Surfaces. In A. Papadopoulos (Ed.), *Handbook of Teichmueller Theory *(Vol. V). European Mathematical Society.

Loftin J, McIntosh I. Cubic Differentials in the Differential Geometry of Surfaces. In Papadopoulos A, editor, Handbook of Teichmueller Theory. Vol. V. European Mathematical Society. 2015

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title = "Cubic Differentials in the Differential Geometry of Surfaces",

abstract = "We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the induced conformal structure: these data come from the Blaschke metric and Pick form for the affine spheres and from the induced metric and second fundamental form for the minimal Lagrangian surfaces. The local geometry, at least for main cases of interest, induces a natural frame whose structure equations arise from the affine Toda system for $\mathfrak a^{(2)}_2$. We also discuss the global theory and applications to representations of surface groups and to mirror symmetry.",

keywords = "math.DG, math.GT, 53C43 (primary), 20H10, 53A15 (secondary)",

author = "John Loftin and Ian McIntosh",

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isbn = "978-3-03719-160-6",

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editor = "Athanase Papadopoulos",

booktitle = "Handbook of Teichmueller Theory",

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T1 - Cubic Differentials in the Differential Geometry of Surfaces

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AU - McIntosh, Ian

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Y1 - 2015

N2 - We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the induced conformal structure: these data come from the Blaschke metric and Pick form for the affine spheres and from the induced metric and second fundamental form for the minimal Lagrangian surfaces. The local geometry, at least for main cases of interest, induces a natural frame whose structure equations arise from the affine Toda system for $\mathfrak a^{(2)}_2$. We also discuss the global theory and applications to representations of surface groups and to mirror symmetry.

AB - We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the induced conformal structure: these data come from the Blaschke metric and Pick form for the affine spheres and from the induced metric and second fundamental form for the minimal Lagrangian surfaces. The local geometry, at least for main cases of interest, induces a natural frame whose structure equations arise from the affine Toda system for $\mathfrak a^{(2)}_2$. We also discuss the global theory and applications to representations of surface groups and to mirror symmetry.

KW - math.DG

KW - math.GT

KW - 53C43 (primary), 20H10, 53A15 (secondary)

M3 - Chapter

SN - 978-3-03719-160-6

VL - V

BT - Handbook of Teichmueller Theory

A2 - Papadopoulos, Athanase

PB - European Mathematical Society

ER -