David Sykes

activity

20232025

collaborators

3 papers

math.DG2025

Pre-Kähler structures and finite-nondegeneracy

Omid Makhmali, David Sykes

Motivated by the geometry of Levi degenerate CR hypersurfaces, we define a \emph{pre-Kähler structure} on a complex manifold as a pre-symplectic structure compatible with the almos…

math.CV2024

Models of $2$ -nondegenerate CR hypersurface in $C^{N}$

Jan Gregorovič, Martin Kolář, David Sykes

We show that every point in a uniformly $2$ -nondegenerate CR hypersurface is canonically associated with a model $2$ -nondegenerate structure. The $2$ -nondegenerate models are basic…

math.CV2023

Defining equations of $7$ -dimensional model CR hypersurfaces

Jan Gregorovič, David Sykes

We study CR hypersurfaces in $C^{4}$ that are Levi degenerate with constant rank Levi form, and moreover finitely nondegenerate. Each of these can be described as a deformat…

Pre-Kähler structures and finite-nondegeneracy

Models of 2-nondegenerate CR hypersurface in CN

Defining equations of 7-dimensional model CR hypersurfaces

Models of $2$ -nondegenerate CR hypersurface in $C^{N}$

Defining equations of $7$ -dimensional model CR hypersurfaces