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We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2 to parallelisms thus solving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequence of two principal bundles over the manifold, takes values in the Lie algebra of infinitesimal automorphisms of the quadric… (More)

We extend the results of [11] on embedded CR manifolds of CR dimension and codimension two to abstract partially integrable almost CR manifolds. We prove that points on such manifolds fall into three different classes, two of which (the hyperbolic and the elliptic points) always make up open sets. We prove that manifolds consisting entirely of hyperbolic… (More)

We generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact manifold is determined solely by the underlying contact distribution. Definitions Suppose M is a 6-dimensional… (More)

- Gerd Schmalz, Andrea Spiro
- 2008

In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codi-mension two, i.e. a pair (P, ω), consisting of a principal bundle π : P → M over M and of a Cartan connection form ω over P , satisfying the following property: the (local) CR transformations f : M → M are in… (More)

- Frank de Hoog, Gerd Schmalz, Tim E. Gureyev
- Appl. Math. Lett.
- 2014

- Timur E Gureyev, Yakov I Nesterets, +4 authors Giuliana Tromba
- Optics express
- 2014

It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of… (More)

- Konstantin M Pavlov, Vasily I Punegov, Kaye S Morgan, Gerd Schmalz, David M Paganin
- Scientific reports
- 2017

A deterministic variant of Bragg Coherent Diffraction Imaging is introduced in its kinematical approximation, for X-ray scattering from an imperfect crystal whose imperfections span no more than half of the volume of the crystal. This approach provides a unique analytical reconstruction of the object's structure factor and displacement fields from the 3D… (More)

- Gerd Schmalz, Jan Slovák, JAN SLOVÁK
- 2012

There are only some exceptional CR dimensions and codi-mensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n + 1, n)/P… (More)

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