TITLE: **Geodesics in Nilpotent Lie Groups.**
ABSTRACT:
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
1976.
Beginning with a brief introduction to this method, we will describe
the
geodesic properties of 2-step nilpotent Lie groups. In particular,
we are
interested in a class of 2-step nilpotent Lie groups which are
constructed
from representations of compact semisimple Lie groups. |