$(\lambda,\lambda)$-eigenfunctions on compact manifolds

Thomas Jack Munn; Oskar Riedler

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arXiv · 2409.16932

$(\lambda,\lambda)$-eigenfunctions on compact manifolds

Thomas Jack Munn·Oskar Riedler

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Abstract

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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BibTeX RIS

Thomas Jack Munn, Oskar Riedler. 2024-09-25. $(\lambda,\lambda)$-eigenfunctions on compact manifolds. https://arxiv.org/abs/2409.16932

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