|TITLE: Geodesics in Nilpotent Lie Groups.
The basic goal of the study of the geometry of Lie groups with a
left invariant metric is to describe the geometry of the group in terms of
the associated metric Lie algebra, as first introduced by Milnor in
Beginning with a brief introduction to this method, we will describe
geodesic properties of 2-step nilpotent Lie groups. In particular,
interested in a class of 2-step nilpotent Lie groups which are
from representations of compact semisimple Lie groups.