## 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

### Keywords:

holomorphic nondegeneracy; finite type; real hypersurface
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