GLOBAL HOLOMORPHIC EQUIVALENCE OF SMOOTH SUBMANIFOLDS IN C-N

Let M be a smooth compact manifold and n greater than or equal to 2. G iven a smooth isotopy of embeddings ft:M hooked right arrow C-n (0 les s than or equal to t less than or equal to 1) such that ft(M) subset o f C-n is a totally real and polynomially convex submanifold of C-n for each fixed t, we construct a sequence Phi(j) of holomorphic automorph isms of C-n such that Phi(j) omicron f(0) converges to f(1) and Phi(j) (-1) omicron f(1) converges to f(0) in C-infinity(M) as j --> infinity . We also obtain results on approximating flows of asymptotically holo morphic vector fields by holomorphic automorphisms of C-n.