Isometric rigidity of submanifolds in products of space forms
Algebraic, topological and analytical techniques in differential geometry and geom...
Group actions, submanifold theory and global analysis in Riemannian and pseudo-Rie...
| Full text | |
| Author(s): |
Dajczer, M.
;
Jimenez, M. I.
;
Vlachos, Th.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Annali di Matematica Pura ed Applicata; v. N/A, p. 14-pg., 2025-03-04. |
| Abstract | |
We investigate isometric immersions f: M-n -> Rn+2, n >= 3, of Riemannian manifolds into Euclidean space with codimension two that admit isometric deformations that preserve the metric of the Gauss map. In precise terms, the preservation of the third fundamental form of the submanifold must be ensured throughout the deformation. For minimal isometric deformations of minimal submanifolds this is always the case. Our main result is of a local nature and states that if f is neither minimal nor reducible, then it is a hypersurface of an isometrically deformable hypersurface F: Mn+1 -> Rn+2 such that the deformations of F induce those of f. Moreover, for a particular class of such submanifolds, a complete local parametric description is provided. (AU) | |
| FAPESP's process: | 22/05321-9 - On deformation of submanifolds |
| Grantee: | Miguel Ibieta Jimenez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 23/06762-1 - Infinitesimally Bonnet bendable submanifolds in codimension 2 |
| Grantee: | Miguel Ibieta Jimenez |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |