Abstract: Let Tbe a
homogeneous structure on an n-dimensional
connectedpseudo-Riemannian
manifold With respect to a pseudo-orthonormal
basis for let be
the vector field such that where The homogeneous structure Tis
called specialif
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
Keywords and phrases: pseudo-Riemannian homogeneous spaces, homogeneous pseudo-Riemannian structures.
