Skip to Main content Skip to Navigation
Journal articles

Holomorphic immersions of bi-disks into 9-dimensional real hypersurfaces with Levi signature (2, 2)

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 D ^ in a smooth 9-dimensional real analytic real hypersurface M^9 in C^5 with Levi signature (2, 2) passing through a fixed point. The result is that the lift to M^9 × 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 × U(2). We then provide an example where one of the functions does not identically vanish, thus obstructing holomorphic immersions.
Document type :
Journal articles
Complete list of metadata

https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03286298
Contributor : Joël Merker Connect in order to contact the contributor
Submitted on : Wednesday, July 14, 2021 - 10:48:45 AM
Last modification on : Wednesday, July 21, 2021 - 3:47:17 AM
Long-term archiving on: : Friday, October 15, 2021 - 4:10:13 PM

File

hal-2-lorentzian-M9.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03286298, version 1

Collections

Citation

Wei-Guo Foo, Joël Merker. Holomorphic immersions of bi-disks into 9-dimensional real hypersurfaces with Levi signature (2, 2). International Mathematics Research Notices, Oxford University Press (OUP), In press. ⟨hal-03286298⟩

Share

Metrics

Record views

10

Files downloads

16