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Geometry and representation of the singular symplectic forms

Wojciech Domitrz, Stanisław Janeczko, Zbigniew Pasternak-Winiarski (2003)

Banach Center Publications

In this paper we show to what extent the closed, singular 2-forms are represented, up to the smooth equivalence, by their restrictions to the corresponding singularity set. In the normalization procedure of the singularity set we find the sufficient conditions for the given closed 2-form to be a pullback of the classical Darboux form. We also find the classification list of simple singularities of the maximal isotropic submanifold-germs in the codimension one Martinet's singular symplectic structures....

Geometry of Cyclic and Anticylic Algebras

Igor M. Burlakov, Marek Jukl (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.

Geometry of Markov systems and codimension one foliations

Andrzej Biś, Mariusz Urbański (2008)

Annales Polonici Mathematici

We show that the theory of graph directed Markov systems can be used to study exceptional minimal sets of some foliated manifolds. A C¹ smooth embedding of a contracting or parabolic Markov system into the holonomy pseudogroup of a codimension one foliation allows us to describe in detail the h-dimensional Hausdorff and packing measures of the intersection of a complete transversal with exceptional minimal sets.

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