Nicolae Anghel University of North Texas

The Spectrum of the Dirac Operator on Certain Topological Spheres

The spectral decomposition of the Dirac operator on highly symmetrical spaces, such as spheres, projective spaces, or grassmannians, is completely understood. However, the methods used to settle these cases, usually pertaining to representation theory, are inapplicable, if one looks at even the slightest geometric perturbations of them, such as the ellipsoids with circle symmetry in R^3, for instance. There one must be satisfied with the various bounds that exist on the spectrum. In this talk, which represents work in progress, we will show how classical methods can be used to deal with the spectrum of the Dirac operator on a suitable class of topological spheres, immersed in R^3.