$(λ,λ)$-eigenfunctions on compact manifolds
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909325789757440 |
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| author | Munn, Thomas Jack Riedler, Oskar |
| author_facet | Munn, Thomas Jack Riedler, Oskar |
| contents | In this note we study $(λ,μ)$-eigenfamilies on compact Riemannian manifolds when $λ= μ$. We show that any compact manifold admitting a $(λ,λ)$-eigenfunction is a mapping torus and that any $(λ,λ)$-eigenfamily is one dimensional. Additionally, we consider generalised eigenfamilies, which can have higher dimension, and relate these to harmonic Riemannian submersions to a torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $(λ,λ)$-eigenfunctions on compact manifolds Munn, Thomas Jack Riedler, Oskar Differential Geometry 53C35, 53C43, 58E20 In this note we study $(λ,μ)$-eigenfamilies on compact Riemannian manifolds when $λ= μ$. We show that any compact manifold admitting a $(λ,λ)$-eigenfunction is a mapping torus and that any $(λ,λ)$-eigenfamily is one dimensional. Additionally, we consider generalised eigenfamilies, which can have higher dimension, and relate these to harmonic Riemannian submersions to a torus. |
| title | $(λ,λ)$-eigenfunctions on compact manifolds |
| topic | Differential Geometry 53C35, 53C43, 58E20 |
| url | https://arxiv.org/abs/2409.16932 |