Convergent Normal Form for Five Dimensional Totally Nondegenerate CR Manifolds in $$\pmb {{\mathbb {C}}^4}$$
| Autor: | Masoud Sabzevari |
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| Rok vydání: | 2021 |
| Předmět: |
Normalization (statistics)
Pure mathematics Class (set theory) Mathematics::Complex Variables Infinitesimal 010102 general mathematics Dimension (graph theory) Automorphism 01 natural sciences Differential geometry 0103 physical sciences Equivariant map 010307 mathematical physics Geometry and Topology 0101 mathematics Equivalence (measure theory) Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 31:7900-7946 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-020-00558-0 |
| Popis: | Applying the equivariant moving frames method, we construct a convergent normal form for real-analytic 5-dimensional totally nondegenerate submanifolds of $${\mathbb {C}}^4$$ . We develop this construction by applying further normalizations, the possibility of which completely relies upon vanishing/non-vanishing of some specific coefficients of the normal form. This in turn divides the class of our CR manifolds into several biholomorphically inequivalent subclasses, each of them has its own specified normal form with no further possible normalization applicable on it. It also is shown that, biholomorphically, Beloshapka’s cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question. |
| Databáze: | OpenAIRE |
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