2012/01/27 by Andreas Hermann, Hermann, Andreas
Mathematics · #53C27 (Primary) 53C21 #58J05 (Secondary) #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1201.5771
openalex publication_date 2012/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non-harmonic 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.