6 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 almo…
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…
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…
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…
Lewy curves in para-CR geometry
Wojciech KryÅski, 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…
A characterization of chains in dimension three
Wojciech KryÅski, 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…