The index of cubic focal manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913022225678336 |
|---|---|
| author | Rauchenberger, Niklas Semmelmann, Uwe |
| author_facet | Rauchenberger, Niklas Semmelmann, Uwe |
| contents | We calculate the index and nullity of the three orientable focal manifolds of isoparametric hypersurfaces in spheres with three distinct principal curvatures. It turns out that the index is equal to the dimension of the ambient Euclidean space and the nullity is completely determined by the normal part of Killing vector fields of the ambient sphere. In that sense, the Veronese embeddings of the projective planes are as stable as possible for non totally geodesic submanifolds of the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The index of cubic focal manifolds Rauchenberger, Niklas Semmelmann, Uwe Differential Geometry 53A10, 53C35 We calculate the index and nullity of the three orientable focal manifolds of isoparametric hypersurfaces in spheres with three distinct principal curvatures. It turns out that the index is equal to the dimension of the ambient Euclidean space and the nullity is completely determined by the normal part of Killing vector fields of the ambient sphere. In that sense, the Veronese embeddings of the projective planes are as stable as possible for non totally geodesic submanifolds of the sphere. |
| title | The index of cubic focal manifolds |
| topic | Differential Geometry 53A10, 53C35 |
| url | https://arxiv.org/abs/2604.09802 |