An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918159940845568 |
|---|---|
| author | Birtea, Petre Casu, Ioan Comanescu, Dan |
| author_facet | Birtea, Petre Casu, Ioan Comanescu, Dan |
| contents | We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace-Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold Birtea, Petre Casu, Ioan Comanescu, Dan Differential Geometry Mathematical Physics 53C30, 15B10, 53Bxx, 58Cxx We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework of Laplace operators on constraint manifolds, we provide the formula for the Laplace-Beltrami operator in terms of the ambient Euclidean coordinates. The result extends previously known cases, recovering the formulas for the sphere and the special orthogonal group as particular instances. |
| title | An explicit formula for the Laplace-Beltrami operator on the Stiefel manifold |
| topic | Differential Geometry Mathematical Physics 53C30, 15B10, 53Bxx, 58Cxx |
| url | https://arxiv.org/abs/2509.18877 |