9 citations · 20 across the 9 of their papers we have counts for
9 papers
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…
Weyl metrizability of 3-dimensional projective structures and CR submanifolds
Omid Makhmali
A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as…
Lewy curves in para-CR geometry
Wojciech Kryński, Omid Makhmali
We define a class of curves, referred to as Lewy curves, in para-CR geometry, following H. Lewy's original definition in CR geometry. We give a characterization of path geometries…
Zero-curvature subconformal structures and dispersionless integrability in dimension five
Boris Kruglikov, Omid Makhmali
We extend the recent paradigm "Integrability via Geometry" from dimensions 3 and 4 to higher dimensions, relating dispersionless integrability of partial differential equations to…
A characterization of chains in dimension three
Wojciech Kryński, Omid Makhmali
Given a 3-dimensional (para-)CR structure, its family of chains define a 3-dimensional path geometry. We provide necessary and sufficient conditions that determine whether a path g…
Parabolic quasi-contact cone structures with an infinitesimal symmetry
Omid Makhmali, Katja Sagerschnig
We interpret the property of having an infinitesimal symmetry as a variational property in certain geometric structures. This is achieved by establishing a one-to-one correspondenc…
Para-Kähler-Einstein 4-manifolds and non-integrable twistor distributions
Gil Bor, Omid Makhmali, Paweł Nurowski
We study the local geometry of 4-manifolds equipped with a \emph{para-Kähler-Einstein} (pKE) metric, a special type of split-signature pseudo-Riemannian metric, and their associate…
The Cayley cubic and differential equations
Wojciech Kryński, Omid Makhmali
We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conforma…
Differential Geometric Aspects of Causal Structures
Omid Makhmali
This article is concerned with causal structures, which are defined as a field of tangentially non-degenerate projective hypersurfaces in the projectivized tangent bundle of a mani…