Non-compact inaudibility of Naturally Reductive property
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912672428064768 |
|---|---|
| author | Arias-Marco, Teresa Fernández-Barroso, José-Manuel |
| author_facet | Arias-Marco, Teresa Fernández-Barroso, José-Manuel |
| contents | Naturally reductive manifolds are an important class of Riemannian manifolds because they provide examples that generalize the locally symmetric ones. A property is said to be inaudible if there exists a unitary operator which intertwines the Laplace-Beltrami operator of two Riemannian manifolds such that one of them satisfies the property and the other does not.
In this paper, we study the relation between 2-step nilpotent Lie groups and the naturally reductive property to prove that this property is inaudible, using a pair of non-compact 11-dimensional generalized Heisenberg groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-compact inaudibility of Naturally Reductive property Arias-Marco, Teresa Fernández-Barroso, José-Manuel Differential Geometry Spectral Theory 58J53, 53C25, 58J50 Naturally reductive manifolds are an important class of Riemannian manifolds because they provide examples that generalize the locally symmetric ones. A property is said to be inaudible if there exists a unitary operator which intertwines the Laplace-Beltrami operator of two Riemannian manifolds such that one of them satisfies the property and the other does not. In this paper, we study the relation between 2-step nilpotent Lie groups and the naturally reductive property to prove that this property is inaudible, using a pair of non-compact 11-dimensional generalized Heisenberg groups. |
| title | Non-compact inaudibility of Naturally Reductive property |
| topic | Differential Geometry Spectral Theory 58J53, 53C25, 58J50 |
| url | https://arxiv.org/abs/2510.23263 |