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On a natural algebraic affine connection on the space of almost complex structures and the curvature of teichmüller space with respect to its Weil-Petersson metric

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Abstract

A formula for the sectional curvature of Teichmüller space with respect to the Weil-Petersson metric is derived in terms of the Laplace-Beltrami operator on functions. It will be shown that the sectional curvature as well as the holomorphic sectional curvature and Ricci curvature are negative. Bounds on the holomorphic and the Ricci curvature are given.

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Authors and Affiliations

  1. Max Planck Institut für Mathematik, Bonn

    A. J. Tromba

  2. University of California Santa Cruz, Bonn

    A. J. Tromba

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  1. A. J. Tromba
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Tromba, A.J. On a natural algebraic affine connection on the space of almost complex structures and the curvature of teichmüller space with respect to its Weil-Petersson metric. Manuscripta Math 56, 475–497 (1986). https://doi.org/10.1007/BF01168506

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  • DOI: https://doi.org/10.1007/BF01168506

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