论文标题
在同质3杆的狄拉克频谱上
On the Dirac spectrum of homogeneous 3-spheres
论文作者
论文摘要
我们表明，$ s^3 \ cong \ operatoRatorname {su}（2）$上的任何两个剩余的指标，对于关联的经典狄拉克运算符$ d $都是等值的。在正常标态曲率的左右指标的情况下，我们计算并使用$ d^2 $的最小特征值。我们在$ \ operatatorName {so}（3）= s^3/\ {\ pm1 \} $上显示了剩余不变的指标的类似结果。
We show that any two left-invariant metrics on $S^3\cong\operatorname{SU}(2)$ which are isospectral for the associated classical Dirac operator $D$ must be isometric. In the case of left-invariant metrics of positive scalar curvature, we compute and use the smallest eigenvalue of $D^2$. We show analogous results for left-invariant metrics on $\operatorname{SO}(3)=S^3/\{\pm1\}$ for each of its two spin structures.
