Geodesic graphs on the 13–dimensional group of Heisenberg type

✍ Scribed by Z. Dušek; O. Kowalski

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 155 KB
• Volume: 254-255
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310054

✦ Synopsis

Abstract

A g.o. space is a homogeneous Riemannian manifold M = (G/H, g) on which every geodesic is an orbit of a one–parameter subgroup of the group G. (G acts transitively on M as a group of isometries.) Each g.o. space gives rise to certain rational maps called “geodesic graphs”. We are particularly interested in the case when the geodesic graphs are of nonlinear character.

Up to recently only linear geodesic graphs and nonlinear geodesic graphs of degree two were observed. Here we study the generalized Heisenberg group (in the sense of A. Kaplan) of dimension 13 and with 5–dimensional center. We show that this is a g.o. space for which the lowest degree of a geodesic graph is equal to six or three, depending on the choice of the isometry group G.