2014/11/20 by Bekkara, Samir, Zeghib, Abdelghani · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1411.5709
The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension ≥ 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.