论文标题
$ 2 $ - nodal域定理，用于高维圆形捆绑
$2$-nodal domain theorems for higher dimensional circle bundles
论文作者
论文摘要
我们证明，非平凡的主捆绑$ s^1 $捆绑包的一般捆绑指标的真实部分（但非不变）特征函数上任何维数的歧管都具有连接的节点集和正好是2个节点域。这概括了作者在$ 3 $维情况下的早期结果。一个参数的旋转子组在固定点集由两个抗突击点组成的旋转子组上说明了非免费$ s^1 $动作的结果的失败。
We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^1$ bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This generalizes earlier results of the authors in the $3$-dimensional case. The failure of the results on for non-free $S^1$ actions is illustrated on even dimensional spheres by one-parameter subgroups of rotations whose fixed point set consists of two antipodal points.
