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 Lp eigenspinor for 0 < p < 2 if the eigenvalue has nontrivial real part, and no nontrivial L2 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.
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Dedicate to Professor Su Buqing for his great achievements in mathematical research and education
This work was supported by the Special Foundations for Guangxi Ba Gui Scholars and Junwu Scholars of Guangxi University.
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Chen, J., Xue, X. & Zhang, X. The Dirac Equation on Metrics of Eguchi-Hanson Type II with Negative Constant Scalar Curvature. Chin. Ann. Math. Ser. B 44, 893–912 (2023). https://doi.org/10.1007/s11401-023-0050-9
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DOI: https://doi.org/10.1007/s11401-023-0050-9