Manifold submetries from compact homogeneous spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917154280964096 |
|---|---|
| author | Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco |
| author_facet | Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco |
| contents | We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of algebraic functions preserved by the Laplace--Beltrami operator, and manifold submetries.
A key intermediate result is that, for any manifold submetry on a compact normal homogeneous space, the vector field given by the mean curvature of the fibers is basic, in the sense that it is related to a vector field in the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manifold submetries from compact homogeneous spaces Lin, Samuel Mendes, Ricardo A. E. Radeschi, Marco Differential Geometry Commutative Algebra Analysis of PDEs Spectral Theory 53C12 (Primary), 53C20, 53C21, 57S15, 58J50, 13A50 (Secondary) We show that singular Riemannian foliations, or, more generally, manifold submetries, defined on a compact normal homogeneous space, have algebraic nature. Moreover, in this case there exists a one-to-one correspondence between algebras of algebraic functions preserved by the Laplace--Beltrami operator, and manifold submetries. A key intermediate result is that, for any manifold submetry on a compact normal homogeneous space, the vector field given by the mean curvature of the fibers is basic, in the sense that it is related to a vector field in the base. |
| title | Manifold submetries from compact homogeneous spaces |
| topic | Differential Geometry Commutative Algebra Analysis of PDEs Spectral Theory 53C12 (Primary), 53C20, 53C21, 57S15, 58J50, 13A50 (Secondary) |
| url | https://arxiv.org/abs/2512.16606 |