Flat Projective Structures on Surfaces and Cubic Holomorphic Differentials

2006/11/09 by François Labourie, F. Labourie, Labourie, F. · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.DG

paper · pdf · doi:10.48550/arxiv.math/0611250

41 pages

arxiv created 2006/11/09 · openalex publication_date 2006/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge theory. We shall also give an application of these results as the uniqueness of a minimal surface in a symmetric space.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Cited by

• Equiaffine immersions and pseudo-Riemannian space forms
• Affine Deformations of Divisible Convex Cones and Affine Spacetimes
• Symplectic geometry of projective structures on surfaces with boundary

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