  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.
