 
Summary: Proceedings Ist International Meeting
on Geometry and Topology
Braga (Portugal)
Public. Centro de Matem´atica
da Universidade do Minho
p. 113, 1998
On Lie Groups with Left Invariant semiRiemannian Metric
R. P. Albuquerque
1 Introduction and General Results
J. Milnor in the well known [2] gave several results concerning curvatures of
left invariant Riemannian metrics on Lie groups. Some of those results can be
partial or totally generalized to indefinite metrics. We will first show three of
those generalizations that we have obtained. These will serve our purposes later
on.
Let G be a real Lie group of dimension n and g its Lie algebra. Considering a
left invariant semiRiemannian structure on G, let e1, . . . , en be an orthonormal
basis of left invariant vector fields and ijk their structure constants, that is,
[ei, ej] =
n
k=1
