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

Stanton, Nancy K.

Am. J. Math. 118, No. 1, 209-233 (1996).

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

Keywords:

holomorphic nondegeneracy; finite type; real hypersurface