On the generic Simplicity of the spectrum for Connection Laplacian and $G$-simplicity on Principal Bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912903047675904 |
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| author | Brito, Geovane C. Marrocos, Marcus A. M. |
| author_facet | Brito, Geovane C. Marrocos, Marcus A. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12884 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the generic Simplicity of the spectrum for Connection Laplacian and $G$-simplicity on Principal Bundles Brito, Geovane C. Marrocos, Marcus A. M. Differential Geometry Primary 58J50, Secondary 55R25 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. |
| title | On the generic Simplicity of the spectrum for Connection Laplacian and $G$-simplicity on Principal Bundles |
| topic | Differential Geometry Primary 58J50, Secondary 55R25 |
| url | https://arxiv.org/abs/2602.12884 |