The Dirac Equation on Metrics of Eguchi-Hanson Type II with Negative Constant Scalar Curvature

On metrics of Eguchi-Hanson type II with negative constant Ricci curvatures, the authors show that there is no nontrivial Killing spinor. On metrics of Eguchi-Hanson type II with negative constant scalar curvature, they show that there is no nontrivial L p eigenspinor for 0 < p < 2 if the eigenvalue has nontrivial real part, and no nontrivial L 2 eigenspinor if either the eigenvalue has trivial real part or the eigenvalue is real, the eigenspinor is isotropic and the parameter η in radial and angular equations for eigenspinors is real. They also solve harmonic spinors and eigenspinors explicitly on metrics of Eguchi-Hanson type II with certain special potentials.