English

On Rigidity of Generalized Conformal Structures

Differential Geometry 2017-01-10 v2

Abstract

The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension 3\geq 3. Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined by its 2-jet at any point. We prove here a similar rigidity for generalized conformal structures defined by giving a one parameter family of metrics (instead of scalar multiples of a given one) on each tangent space.

Keywords

Cite

@article{arxiv.1411.5709,
  title  = {On Rigidity of Generalized Conformal Structures},
  author = {Samir Bekkara and Abdelghani Zeghib},
  journal= {arXiv preprint arXiv:1411.5709},
  year   = {2017}
}
R2 v1 2026-06-22T07:06:36.868Z