Rigidity of CR-immersions into Spheres

摘要

We consider local CR-immersions of a strictly pseudoconvex real hypersurface M is contained in C~(n+1), near a point p ∈ M, into the unit sphere S is contained in C~(n+d+1) with d > 0. Our main result is that if there is such an immersion f : (M,p) → S and d < n/2, then f is rigid in the sense that any other immersion of (M,p) into S is of the form φ ° f, where φ is a biholomorphic automorphism of the unit ball B is contained in C~(n+d+1). As an application of this result, we show that an isolated singulary of an irreducible analytic variety of codimension d in C~(n+d+1) is uniquely determined up to affine linear transformations by the local CR geometry at a point of its Milnor link.