1-rigidity of CR submanifolds in spheres
| dc.creator | Wang, Sung Ho | |
| dc.date | 2005-06-08 | |
| dc.date | 2005-08-16 | |
| dc.date.accessioned | 2026-07-07T05:20:35Z | |
| dc.date.available | 2026-07-07T05:20:35Z | |
| dc.description | We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It measures how a deformation deviates from a one parameter family of motions up to 1st order. We implement this method to rigidity of CR submanifolds in spheres. A class of submanifolds called Bochner rigid submanifolds are shown to be 1-rigid under type preserving CR deformations. This 1-rigidity is then extended to a local rigidity, which roughly states that if a CR submanifold $ M$ is Bochner rigid, then any CR submanifold that is sufficiently close and CR equivalent to $ M$ is congruent to $ M$ by an automorphism of the sphere. | |
| dc.description | 43 pages | |
| dc.identifier | https://arxiv.org/abs/math/0506134 | |
| dc.identifier | http://arxiv.org/abs/math/0506134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75430 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 53B25, 32V30 | |
| dc.title | 1-rigidity of CR submanifolds in spheres | |
| dc.type | text |