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 . 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.
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}
}