4 research outputs found
On Rigidity of Generalized Conformal Structures
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
Contents
Abstract. We analyze sub-Riemannian and lightlike metrics from the point of view of their rigidity as geometric structures. Following Cartan’s and Gromov’s formal definitions, they are never rigid, yet, in generic cases, they naturally give rise to rigid geometri