(\lambda,\lambda)$-eigenfunctions on compact manifolds
In this note we study $(\lambda,\mu)$-eigenfamilies on compact Riemannian manifolds when $\lambda = \mu$. We show that any compact manifold admitting a $(\lambda,\lambda)$-eigenfunction is a mapping torus and that any $(\lambda,\lambda)$-eigenfamily is one dimensional. Additionally, we consider gene...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
25-09-2024
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | In this note we study $(\lambda,\mu)$-eigenfamilies on compact Riemannian
manifolds when $\lambda = \mu$. We show that any compact manifold admitting a
$(\lambda,\lambda)$-eigenfunction is a mapping torus and that any
$(\lambda,\lambda)$-eigenfamily is one dimensional. Additionally, we consider
generalised eigenfamilies, which can have higher dimension, and relate these to
harmonic Riemannian submersions to a torus. |
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| DOI: | 10.48550/arxiv.2409.16932 |