JP Journal of Geometry and Topology
Volume 8, Issue 3, Pages 203 - 228
(November 2008)
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SPECIAL HOMOGENEOUS STRUCTURES ON PSEUDO-RIEMANNIAN MANIFOLDS
Barbara De Leo (Italy) and Rosa Anna Marinosci (Italy)
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With respect to a pseudo-orthonormal
basis
for
let
be
the vector field such that
where
The homogeneous structure T is
called special if
We prove that all homogeneous
structures on a compact orientable pseudo-Riemannian manifold are special.
We obtain the same result in the general case when the vector field
naturally
associated to the homogeneous pseudo-Riemannian T,
is a conformal Killing vector field. All homogeneous pseudo-Riemannian
structures of the class
are
special;
they are characterized by the condition
New examples of homogeneous
pseudo-Riemannian structures of the class
are
given.
Finally, we consider
Lorentzian homogeneous structures on three-dimensional Lorentzian Lie groups. As
a result of our study, we find that all three-dimensional Lorentzian unimodular
Lie groups always admit a Lorentzian homogeneous structure of the class
The
non-unimodular case is also considered. We prove that each three-dimensional
Lorentzian non-unimodular Lie group satisfying a supplementary condition, admits
a Lorentzian homogeneous structure of the class
or of the class
