The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits

Details The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits The Geometry of K-Orbits of a Subclass of MD5-Groups and Foliations Formed by their Generic K-Orbits

2006-03-03

arxiv.org/abs/math/0603089v1

Mathematics

Differential Geometry

24 pages, no figue

Scientific paper

The present paper is a continuation of Le Anh Vu's ones [13], [14], [15]. Specifically, the paper is concerned with the subclass of connected and simply connected MD5-groups such that their MD5-algebras $\mathcal{G}$ have the derived ideal ${\mathcal{G}}^{1} : = [ \mathcal{G},\mathcal{G} ]\equiv$ ${\bf{R}}^{3}$. We shall describe the geometry of K-orbits of these MD5-groups. The foliations formed by K-orbits of maximal dimension of these MD5-groups and their measurability are also presented in the paper.

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