Hermann, Andreas (2012) Dirac eigenspinors for generic metrics. Preprintreihe der Fakultät Mathematik 12/2012, Working Paper.
We consider a Riemannian spin manifold (M, g) with a fixed spin structure. The zero sets of solutions of generalized Dirac equations on M play an important role in some questions arising in conformal spin geometry and in mathematical physics. In this setting the mass endomorphism has been defined as the constant term in an expansion of Green's function for the Dirac operator. One is interested in obtaining metrics, for which it is not zero.
In this thesis we study the dependence of the zero sets of eigenspinors of the Dirac operator on the Riemannian metric. We prove that on closed spin manifolds of dimension 2 or 3 for a generic Riemannian metric the nonharmonic eigenspinors have no zeros. Furthermore we prove that on closed spin manifolds of dimension 3 the mass endomorphism is not zero for a generic Riemannian metric.
|Item Type:||Monograph (Working Paper)|
|Institutions:||Mathematics > Prof. Dr. Bernd Ammann|
|Keywords:||Spin geometry, Dirac operators, spectrum, eigenspinors|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||30 Jul 2012 08:19|
|Last Modified:||30 Jul 2012 08:19|