A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus
Copyright policy )A comparison of the eigenvalues of the Dirac and Laplace operators on a two-dimensional torus
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.
Latex2.09, 28 pages, with figures
- University of Freiburg Germany
- Humboldt-Universität zu Berlin Germany
Mathematics - Differential Geometry, Surfaces in Euclidean and related spaces, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Sturm-Liouville, Mathieu spinors, 58G25, 53A05, Hamiltonian
Mathematics - Differential Geometry, Surfaces in Euclidean and related spaces, Differential Geometry (math.DG), Spectral problems; spectral geometry; scattering theory on manifolds, FOS: Mathematics, Sturm-Liouville, Mathieu spinors, 58G25, 53A05, Hamiltonian
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