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Infinitesimal CR automorphisms of real hypersurfaces. (English) Zbl 0849.32012

A real-analytic real hypersurface \(M\) through the origin in \(\mathbb{C}^{n + 1}\) is said to be holomorphically nondegenerate at the origin if there is no nontrivial holomorphic vector field tangent to \(M\) in a neighborhood of the origin. This condition is necessary and sufficient for the finite-dimensionality of the space of infinitesimal CR automorphisms defined in some neighborhood of the origin in \(M\) that are of the form \(X = Re\) \(Z\) for some holomorphic vector field \(Z\). The other main result is a criterion for a hypersurface \(M\) to be holomorphically degenerate at the origin.
Reviewer: J.S.Joel (Kelly)

MSC:

32V40 Real submanifolds in complex manifolds
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