Abstract
AbstractFor Riemannian submersions with fibers of basic mean curvature, we compare the spectrum of the total space with the spectrum of a Schrödinger operator on the base manifold. Exploiting this concept, we study submersions arising from actions of Lie groups. In this context, we extend the state-of-the-art results on the bottom of the spectrum under Riemannian coverings. As an application, we compute the bottom of the spectrum and the Cheeger constant of connected, amenable Lie groups.
Funder
Max Planck Institute for Mathematics
Publisher
Springer Science and Business Media LLC
Reference23 articles.
1. Baider, A.: Noncompact Riemannian manifolds with discrete spectra. J. Differ. Geom. 14(1), 41–57 (1979)
2. Ballmann, W., Matthiesen, H., Polymerakis, P.: On the bottom of spectra under coverings. Math. Z. 288(3–4), 1029–1036 (2018)
3. Ballmann, W., Polymerakis, P.: Bottom of spectra and coverings. Surv. Differ. Geom. 23, 1–33 (2020)
4. Bessa, G.P., Montenegro, J.F., Piccione, P.: Riemannian submersions with discrete spectrum. J. Geom. Anal. 22(2), 603–620 (2012)
5. Bordoni, M.: Spectral estimates for submersions with fibers of basic mean curvature. An. Univ. Vest Timiş. Ser. Mat.-Inform. 44(1), 23–36 (2006)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On the Spectrum of Certain Hadamard Manifolds;Symmetry, Integrability and Geometry: Methods and Applications;2023-07-23
2. On the Steklov spectrum of covering spaces and total spaces;Annals of Global Analysis and Geometry;2023-01-17