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

作者：Junwen CHEN; Xiaoman XUE; Xiao ZHANG

来源：Chinese Annals of Mathematics Series B, 2023, 44(06): 893-912.

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.

• 单位
  中国科学院数学与系统科学研究院; 广西大学; 中国科学院大学