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Hayashimoto, Atsushi; van Thu, Ninh

Infinitesimal CR automorphisms and stability groups of infinite-type models in \(\mathbb{C}^2\). (English) Zbl 1351.32060

Kyoto J. Math. 56, No. 2, 441-464 (2016).
The authors study the local automorphisms of rigid hypersurfaces of infinite type in \(\mathbb C^2\). The results depend on whether the infinite-type degeneracy of the Levi form occurs on an isolated line or not. In the former case the Lie algebra of infinitesimal automorphisms splits into the obvious (due to rigidity) translation part and a possible stability part. Theorem 2 deals with the case of a second translation symmetry, which causes the degeneracy to extend along a plane. This implies that the stability group vanishes. In Theorem 3, the authors show that the presence of a infinitesimal rotation symmetry implies that the defining function of a rigid infinite type hypersurface is rotationally invariant.
Reviewer: Gerd Schmalz (Armidale)

Cited in 2 Documents

MSC:

32V40 Real submanifolds in complex manifolds
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables

Keywords:

holomorphic vector field; automorphism group; real hypersurface; infinite-type point
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References:

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