Reflection about k-jets and holomorphic extension of CR mappings

Let f :M →M1 be a CR mapping between real analytic generic submanifolds M, M1 of CN and CN1 , respectively. According to Webster’s theory (Proc. Amer. Math. Soc. 86 (1982) 236–240) and its further developments, f has holomorphic extension to a full neighborhood of M in CN when the following requirements are fulfilled: f extends to a wedge W continuous up to M; f is of class Ck; f T CM = T CM1 (where T C denotes the complex tangent bundle); M1 is “k-nondegenerate.” We deal here with the case where f T CM is strictly smaller than T CM1 but is still real analytic in suitable sense.We show that a suitably refined condition of k-nondegeneracy still entails holomorphic extension of f .  2003 Elsevier Inc. All rights reserved.