Stationary discs and finite jet determination for CR mappings in higher codimension (Q776824)

It is well known that for the 2-jet determination of the automorphisms of a CR manifold it is necessary to assume that the manifold is Levi generating and Levi nondegenerate at the reference point. Meylan's recent example showed that this condition is not sufficient for CR manifolds of codimension at least 5 and reopened the question of a criterion for 2-jet determination. There is a number of sufficient (but not necessary) conditions. In the paper under review the author considers strongly pseudoconvex CR manifolds. 2-jet determination was known for real-analytic, strongly pseudoconvex, Levi-generating (e.g. by previous work of the author). The author applies the method of stationary discs to prove that a \(\mathcal C^2\)-smooth CR diffeomorphism of two \(\mathcal C^4\)-smooth strictly pseudoconvex Levi generating CR manifolds is determined by its 2-jet at a given point.