Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds

In this paper we analyze the eigenvalues and eigenfunctions of the Hodge Laplacian for generic metrics on a closed 3-manifold M. In particular, we show that the nonzero eigenvalues are simple and the zero set of the eigenforms of degree $1$ or $2$ consists of isolated points for a residual set of Cʳ metrics on M, for any integer r 2. The proof of this result hinges on a detailed study of the Beltrami (or rotational) operator on co-exact $1$-forms.