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Riemannian metrics on Teichmüller space

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Abstract

On each compact Riemann surface Σ of genusp≥1, we have the Bergman metric obtained by pulling back the flat metric on its Jacobian via the Albanese map. Taking theL 2-product of holomorphic quadratic differentials w.r.t. this metric induces a Riemannian metric on the Teichmüller spaceT p that is invariant under the action of the modular group. We investigate geometric properties of this metric as an alternative to the usually employed Weil-Petersson metric.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, 44780, Bochum

    Lutz Habermann & Jürgen Jost

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  1. Lutz Habermann
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  2. Jürgen Jost
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Habermann, L., Jost, J. Riemannian metrics on Teichmüller space. Manuscripta Math 89, 281–306 (1996). https://doi.org/10.1007/BF02567518

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  • DOI: https://doi.org/10.1007/BF02567518

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