Abstract
We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on non-trivial 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.
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