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

by

Ilka Agricola, Bernd Ammann,
Thomas Friedrich

**A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus**
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*Manuscripta Math.* **100**, no. 2, *231-258, 1999*

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.
58G25, 53A05
### Keywords

Dirac operator, Laplace operator, two-torus, surfaces

Bernd Ammann, 12.12.1998