On the generic Simplicity of the spectrum for Connection Laplacian and $G$-simplicity on Principal Bundles
Abstract
In this paper, we prove that, for a residual set of $C^{k}$ connections defined on a smooth vector bundle $E \to M$, all eigenvalues of the connection Laplacian operator $\mathscr{L}$, acting on the space of sections of $E$, are simple. As an application, we prove that all eigenvalues of the Laplace-Beltrami operator on a compact $G$-principal bundle $P \to M$ are $G$-simple.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint