| Full text | |
| Author(s): |
Jimenez, M. I.
;
Tojeiro, R.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 67, n. 1, p. 25-pg., 2024-01-11. |
| Abstract | |
Li, Ma and Wang have provided in [13] a partial classification of the so-called Moebius deformable hypersurfaces, that is, the umbilic-free Euclidean hypersurfaces $f\colon M<^>n\to \mathbb{R}<^>{n+1}$ that admit non-trivial deformations preserving the Moebius metric. For $n\geq 5$, the classification was completed by the authors in [12]. In this article we obtain an infinitesimal version of that classification. Namely, we introduce the notion of an infinitesimal Moebius variation of an umbilic-free immersion $f\colon M<^>n\to \mathbb{R}<^>m$ into Euclidean space as a one-parameter family of immersions $f_t\colon M<^>n\to \mathbb{R}<^>m$, with $t\in (-\epsilon, \epsilon)$ and $f_0=f$, such that the Moebius metrics determined by ft coincide up to the first order. Then we characterize isometric immersions $f\colon M<^>n\to \mathbb{R}<^>m$ of arbitrary codimension that admit a non-trivial infinitesimal Moebius variation among those that admit a non-trivial conformal infinitesimal variation, and use such characterization to classify the umbilic-free Euclidean hypersurfaces of dimension $n\geq 5$ that admit non-trivial infinitesimal Moebius variations. (AU) | |
| FAPESP's process: | 22/16097-2 - Modern methods in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/05321-9 - On deformation of submanifolds |
| Grantee: | Miguel Ibieta Jimenez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |