Homogeneous pseudo-Riemannian structures of class T2 on low-dimensional generalized symmetric spaces

We give a contribution about the study of homogeneous pseudoRiemannian structures on a type of homogeneous spaces, namely, the pseudo-Riemannian generalized symmetric spaces of low dimensions. It is well known that generalized symmetric Riemannian spaces admit homogeneous structures of the class T2 ⊕ T3. The same property holds in the pseudo-Riemannian context. The aim of the present paper is to improve this result, showing that in the pseudo-Riemannian case threeand four-dimensional generalized symmetric spaces, not symmetric, admit homogeneous structures of class T2. M.S.C. 2010: 53C20, 53C30, 53C50