Zero CR-curvature equations for Levi degenerate hypersurfaces via Pocchiola’s invariants
| Autor: | Alexander Isaev |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Rank (linear algebra) Mathematics::Complex Variables 010102 general mathematics Degenerate energy levels Zero (complex analysis) General Medicine Curvature 01 natural sciences Hypersurface 0103 physical sciences Monge equation Mathematics::Differential Geometry 010307 mathematical physics 0101 mathematics Partial classification Mathematics |
| Zdroj: | Annales de la Faculté des sciences de Toulouse : Mathématiques. 28:957-976 |
| ISSN: | 2258-7519 |
| DOI: | 10.5802/afst.1618 |
| Popis: | In our earlier articles we studied tube hypersurfaces in ${\mathbb C}^3$ that are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we showed that the vanishing of the CR-curvature of such a hypersurface is equivalent to the Monge equation with respect to one of the variables. In the present paper we provide an alternative shorter derivation of this equation by utilizing two invariants discovered by S. Pocchiola. We also investigate Pocchiola's invariants in the rigid case and give a partial classification of rigid 2-nondegenerate uniformly Levi degenerate of rank 1 hypersurfaces with vanishing CR-curvature. |
| Databáze: | OpenAIRE |
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