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

Ilka Agricola·Bernd Ammann·Thomas Friedrich
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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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Ilka Agricola, Bernd Ammann, Thomas Friedrich. 1998-12-09. A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. https://arxiv.org/abs/math/9812044

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