Characterizing the harmonic manifolds by the eigenfunctions of the Laplacian
Jaigyoung Choe, Sinhwi Kim, JeongHyeong Park
TL;DR
This paper characterizes harmonic manifolds such as space forms and hyperbolic spaces using specific radial eigenfunctions of the Laplacian, providing a new way to identify these geometric structures.
Contribution
It introduces a characterization of harmonic manifolds based on eigenfunctions of the Laplacian, extending the understanding of their geometric properties.
Findings
Space forms are characterized by specific Laplacian eigenfunctions.
Complex and quaternionic hyperbolic spaces are distinguished as harmonic manifolds.
The approach offers a new spectral perspective on harmonic manifold classification.
Abstract
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.