We develop the classification of weakly symmetric pseudo--riemannian
manifolds G/H where G is a semisimple Lie group and H is a reductive
subgroup. We derive the classification from the cases where G is compact, and
then we discuss the (isotropy) representation of H on the tangent space of
G/H and the signature of the invariant pseudo--riemannian metric. As a
consequence we obtain the classification of semisimple weakly symmetric
manifolds of Lorentz signature (n−1,1) and trans--Lorentz (conformal Lorentz)
signature (n−2,2).Comment: This arXiv version 3 adds a reference to version 2 and tweaks the
Introduction accordingl