Related papers: 3-dimensional methods in contact geometry
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…
3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly…
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…
A PhD thesis written under supervision of Pawel Nurowski and defended at the Faculty of Physics of the University of Warsaw. We adress the problems of local equivalence and geometry of third order ODEs modulo contact, point and…
The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…
The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate…
The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…
In this paper we give a simple application of the filling methods developed earlier to the chord problem in three dimensional contact geometry.
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.
A sketch based 3D shape retrieval
Three-dimensional Ultrasound image segmentation methods are surveyed in this paper. The focus of this report is to investigate applications of these techniques and a review of the original ideas and concepts. Although many two-dimensional…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
Contact geometry has been applied to various mathematical sciences, and it has been proposed that a contact manifold and a strictly convex function induce a dually flat space that is used in information geometry. Here, such a dually flat…
These notes, based on a graduate course I gave at Hamburg University in 2003, are intended to students having basic knowledges of differential geometry. Their main purpose is to provide a quick and accessible introduction to different…
Systems with dissipation can be described using contact geometry. We introduce the concepts of symmetries and dissipation laws for contact Hamiltonian systems and study the relation between them. This is an ongoing collaboration with Xavier…
A complex contact threefold is a threefold with a two-dimensional non-integrable holomorphic distribution. A contact curve on a contact threefold is an integrable curve of the distribution. This work was inspired by two papers of Bryant, in…
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interactions on the 2D triangular lattice, we show that patch test…
These lectures were a part of the geometry course held during the Fall 2011 Mathematics Advanced Study Semesters (MASS) Program at Penn State (\url{http://www.math.psu.edu/mass/}). The lectures are meant to be accessible to advanced…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…