Kahler metric on the space of convex real projective structures on surface

2013/12/06 by Inkang Kim, Инканг Ким, Kim, Inkang +2 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds #Representation Theory (math.RT) #math.AG #math.GT #math.RT

paper · pdf · doi:10.48550/arxiv.1312.1965

10 pages, to appear in JDG

openalex publication_date 2013/12/06 · arxiv created 2016/06/03 · arxiv updated 2016/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the space of convex real projective structures on a surface of genus g≥ 2 admits a mapping class group invariant Kähler metric where Teichmüller space with Weil-Petersson metric is a totally geodesic complex submanifold.

Citations

• The Self-Duality Equations on a Riemann Surface
• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

Cited by

• Convex real projective structures and Weil's local rigidity Theorem

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