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We consider a problem whether a CR mapping of a generic manifold in complexspace is uniquely determined by its finite jet at a point, which is referred toas finite jet determination. We derive the finite jet determination for CRmappings of smooth Levi nondegenerate manifolds of arbitrary codimension fromthe finite dimensionality of the algebras of infinitesimal automorphisms of thecorresponding quadrics. Previously, this implication was known for realanalytic manifolds. We prove a new 2-jet determination result that covers mostaffirmative results on this matter obtained so far.

Infinitesimal automorphisms of quadrics and second jet determination for CR mappings