Conformal infinitesimal variations of submanifolds
Differential Geometry
2021-01-19 v4
Abstract
This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds is a classical subject in differential geometry. In fact, already in 1917 Cartan classified parametrically the Euclidean hypersurfaces that admit nontrivial conformal variations. Our first main result is a Fundamental theorem for conformal infinitesimal variations. The second is a rigidity theorem for Euclidean submanifolds that lie in low codimension.
Keywords
Cite
@article{arxiv.2002.02551,
title = {Conformal infinitesimal variations of submanifolds},
author = {M. Dajczer and M. I. Jimenez},
journal= {arXiv preprint arXiv:2002.02551},
year = {2021}
}
Comments
The title has been changed in the last version