Deforming convex real projective structures

2017/02/02 by Anna Wienhard, Tengren Zhang, Wienhard, Anna +1
Mathematics · #53C10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1702.00580

openalex publication_date 2017/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a closed, connected, orientable surface of genus at least 2, and let C(S) denote the deformation space of convex real projective structures S. In this article, we introduce two new flows on C(S), which we call the internal bulging flow and the eruption flow. These are geometrically defined flows associated to each pair of pants in a pants decomposition on S that deform the internal parameters. We show that the eruption flows, together with the generalized twist flows about the pants curves, give rise to a half-dimensional family of commuting flows on C(S).

Citations

• Bulging deformations of convex RP²-manifolds

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