Nondegeneracy of the eigenvalues of the Hodge Laplacian for generic metrics on 3-manifolds (Q2841350)

Let \(M\) be a compact three-dimensional Riemannian manifold and \(r\geq 2.\) It is the main result of the paper that there is a residual subset \(\Gamma\) of the space of \(C^r\)-metrics such that, for all \(g\in \Gamma,\) the following holds: The non-zero eigenvalues of the Hodge Laplacian \(\Delta_g\) on \(p\)-forms have multiplicity \(1\) for \(0 \leq p\leq 3\) and the zero set of eigenforms of degree \(p=1,2\) are isolated. The authors use a detailed analysis of the Beltrami operator \(\star_g \circ d.\)