  We consider a problem whether a CR mapping of a generic manifold in complex
space is uniquely determined by its finite jet at a point, which is referred to
as finite jet determination. We derive the finite jet determination for CR
mappings of smooth Levi nondegenerate manifolds of arbitrary codimension from
the finite dimensionality of the algebras of infinitesimal automorphisms of the
corresponding quadrics. Previously, this implication was known for real
analytic manifolds. We prove a new 2-jet determination result that covers most
affirmative results on this matter obtained so far.
