Letp be an analytic disc attached to a generating CR-submanifoldM of Cn. It is proved that some recently introduced conditions onp andM which imply that the family of all smallCα holomorphic perturbations ofp alongM is a Banach submanifold of (Aα(D))n are equivalent. These conditions are given in terms of the partial indices of the discp attached toM and “holomorphic sections” of the conormal bundle ofM along p(∂D). Also, a sufficient geometric conditionon p andM is given so that the family of all smallCα holomorphic perturbationsof p alongM, fixed at some boundary point, is a Banach submanifold of (Aα (D))n.
Vector Function Matrix Function Closed Curve Holomorphic Section Common Zero
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