Gerd Schmalz

University of New England (Australia)

CR-Manifolds, Differential Equations and Multicontact Structures

Cartan’s method of moving frames has been successfully applied to the study of CR-manifolds, their mappings and invariants. For some types of CR-manifolds there is a close relation to the point-wise or contact geometry of differential equations. This can be used to find CR-manifolds with special symmetries. The recently introduced notion of multicontact structures provides a general framework comprising certain geometries of differential equations and CR-manifolds which in turn give examples with many symmetries.