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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.

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 codimension 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)

- KANG - TAE KIM, EVGENY POLETSKY, Gerd Schmalz
- 2008

Abstract. The main result of the paper is the following generalization of Forelli’s theorem [F]: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues whose ratios are positive reals. Then any function φ that has an asymptotic Taylor expansion at p and is… (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)

- A. Cap, Michael Eastwood, Gerd Schmalz, Jan Slov
- 2000

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.

- Gerd Schmalz, Jan Slovák, Jan Slovák
- 2012

There are only some exceptional CR dimensions and codimensions 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 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 with… (More)

- Gerd Schmalz
- 2015

*Correspondence: Vladimir.Ejov@flinders.edu.au; schmalz@une.edu.au 1School of Computer Science, Engineering and Mathematics, Flinders University, Sturt Road, Bedford Park, Adelaide SA 5042, Australia 2School of Science and Technology, University of New England, Armidale NSW 2351, Australia Abstract In this paper, we present a complete list of rigid… (More)