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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.13498 |
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Table of Contents:
- 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.