Velling-Kirillov metric on the universal Teichmuller curve

2002/06/19 by Lee-Peng Teo, Teo, Lee-Peng · 2 citations
Mathematics · #30F60 #32G15 #32M10 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.CV #msc:30F60 #msc:32G15 #msc:32M10

paper · pdf · doi:10.48550/arxiv.math/0206202

35 pages

openalex publication_date 2002/06/19 · arxiv created 2002/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Velling's approach and prove that the second variation of the spherical areas of a family of domains defines a Hermitian metric on the universal Teichmuller curve, whose pull back to Diff+(S¹)/S¹ coincides with the Kirillov metric. We show that the vertical integration of the square of the symplectic form of Velling-Kirillov metric on the universal Teichmuller curve is the symplectic form that defines the Weil-Petersson metric on the universal Teichmuller space. Restricted to a finite dimensional Teichmuller space, the vertical integration of the corresponding form on the Teichmuller curve is also the symplectic form that defines the Weil-Petersson metric on the Teichmuller space.

Cited by

• Characterization of Asymptotically Smooth Curves
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