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Spectra of Unit Tangent Bundles of Compact Hyperbolic Riemann Surfaces

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Abstract

Recent results of Gordon, Mao and Pesce imply that isospectral compact hyperbolic Riemann surfaces have Laplace and length isospectral unit tangent bundles. In this note we give explicit formulae relating the spectra of such surfaces and those of their unit tangent bundles, and use them to prove the converses.

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Authors and Affiliations

  1. FaMAF, Ciudad Universitaria, 5000, Córdoba, Argentina

    Marcos Salvai

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  1. Marcos Salvai
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Salvai, M. Spectra of Unit Tangent Bundles of Compact Hyperbolic Riemann Surfaces. Annals of Global Analysis and Geometry 16, 357–370 (1998). https://doi.org/10.1023/A:1006559507739

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