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

Abstract

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.

Keywords

Metric of Eguchi-Hanson type II / Killing spinor / Eigenspinor

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