Isometric rigidity of submanifolds in products of space forms
Hypersurfaces of Symmetric Spaces, Biquotients and Orbifolds
Geometry of manifolds in the euclidian space and in the Minkowski space
| Full text | |
| Author(s): |
And, Marcos Dajczer
;
Jimenez, Miguel Ibieta
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 152, n. 8, p. 9-pg., 2024-06-05. |
| Abstract | |
Classifying the nonflat hypersurfaces in Euclidean space f : M n -> R n+1 that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten in 1928 [Proceedings Amsterdam 31 (1928), pp. 208-218]. He found two conditions that are necessary and sufficient, with the first one being the minimality of the submanifold. The second is a technical condition that does not clarify much about the geometric nature of the hypersurface. In that respect, the parametric solution of the problem given in this note yields that the submanifold has to be Kaehler. (AU) | |
| FAPESP's process: | 22/05321-9 - On deformation of submanifolds |
| Grantee: | Miguel Ibieta Jimenez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |