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A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus

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Abstract:

We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples.

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Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Institut für Mathematik,¶Sitz: Ziegelstraße 13a, Unter den Linden 6, D-10099 Berlin, Germany.¶e-mail: agricola@mathematik.hu-berlin.de; friedric@mathematik.hu-berlin.de, , , , , , DE

    Ilka Agricola & Thomas Friedrich

  2. Universität Freiburg, Mathematisches Institut, Eckerstr. 1, D-79104 Freiburg, Germany. e-mail: ammann@mathematik.uni-freiburg.de, , , , , , DE

    Bernd Ammann

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  1. Ilka Agricola
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  2. Bernd Ammann
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  3. Thomas Friedrich
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Received: 10 December 1998

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Agricola, I., Ammann, B. & Friedrich, T. A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus. manuscripta math. 100, 231–258 (1999). https://doi.org/10.1007/s002290050239

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  • DOI: https://doi.org/10.1007/s002290050239

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