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Infinitesimal symmetries of weakly pseudoconvex manifolds
- Source :
- Mathematische Zeitschrift 300, 2022
- Publication Year :
- 2019
-
Abstract
- We classify the Lie algebras of infinitesimal CR automorphisms of weakly pseudoconvex hypersurfaces of finite multitype in $\mathbb C^N$. In particular, we prove that such manifolds admit neither nonlinear rigid automorphisms, nor real or nilpotent rotations. As a consequence, this leads to a proof of a sharp 2-jet determination result for local automorphisms. Moreover, for hypersurfaces which are not balanced, CR automorphisms are uniquely determined by their 1-jets. The same classification is derived also for special models, given by sums of squares of polynomials. In particular, in the case of homogeneous polynomials the Lie algebra of infinitesimal CR automorphisms is always three graded. The results provide an important necessary step for solving the local equivalence problem on weakly pseudoconvex manifolds.<br />Comment: 14 pages
- Subjects :
- Mathematics - Complex Variables
Subjects
Details
- Database :
- arXiv
- Journal :
- Mathematische Zeitschrift 300, 2022
- Publication Type :
- Report
- Accession number :
- edsarx.1905.06456
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00209-021-02873-w