Hyperspaces that satisfy cc-homogeneous cone condition on canonical Heisenberg and Engel groups

Besicovitch Covering Property for Homogeneous Distances on the Heisenberg Groups

We prove that the Besicovitch Covering Property (BCP) holds for homogeneous distances on the Heisenberg groups whose unit ball centered at the origin coincides with an Euclidean ball. We provide therefore the first examples of homogeneous distances that satisfy BCP in these groups. Indeed, commonly used homogeneous distances, such as (Cygan-)Korányi and Carnot-Carathéodory distances, are known ...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Einstein metrics: Homogeneous solvmanifolds, generalised Heisenberg groups and Black Holes

In this paper we construct Einstein spaces with negative Ricci curvature in various dimensions. These spaces – which can be thought of as generalised AdS spacetimes – can be classified in terms of the geometry of the horospheres in Poincaré-like coordinates, and can be both homogeneous and static. By using simple building blocks, which in general are homogeneous Einstein solvmanifolds, we give ...

un 2 00 4 Notes on Engel groups and Engel elements in groups . Some generalizations

Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent groups and nilpo-tent radicals in groups. These notions generate problems which are parallel to Burnside problems for periodic groups. The first three theorems of the paper are devoted to nil-groups and Engel groups, w...

More about Embeddings of Almost Homogeneous Heisenberg Groups

Heisenberg groups are simply connected nilpotent Lie groups of class 2. A group is called almost homogeneous if its automorphism group acts with at most 3 orbits. Several open problems about the existence of embeddings between almost homogeneous Heisenberg groups have been posed in a previous paper by the second author. Most of these problems are solved. Mathematics Subject Classification 2000:...