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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