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- Title
Holomorphic Immersions of Bi-Disks into 9D Real Hypersurfaces with Levi Signature (2,2).
- Authors
Foo, Wei Guo; Merker, Joël
- Abstract
Inspired by an article of R. Bryant on holomorphic immersions of unit disks into Lorentzian CR manifolds, we discuss the application of Cartan's method to the question of the existence of bi-disk |$\mathbb{D}^{2}$| in a smooth |$9$| D real-analytic real hypersurface |$M^{9}\subset \mathbb{C}^{5}$| with Levi signature |$(2,2)$| passing through a fixed point. The result is that the lift to |$M^{9}\times U(2)$| of the image of the bi-disk in |$M^{9}$| must lie in the zero set of two complex-valued functions in |$M^{9}\times U(2)$|. We then provide an example where one of the functions does not identically vanish, thus obstructing holomorphic immersions.
- Subjects
MATTHEW, the Apostle, Saint; IMMERSIONS (Mathematics); HYPERSURFACES
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 7, p5466
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa266