The mandala of Legendrian dualities for pseudo-spheres \ud in Lorentz-Minkowski space and "flat'' spacelike surfaces

Using the Legnedrian duarities between surfaces\ud in pseudo-spheres in Lorentz-{Minkow}{ski} 4-space,\ud we study various kind of flat surfaces in\ud pseudo-spheres.\ud We consider a surface in the pseudo-sphere and\ud its dual surface.\ud Flatness of a surface is defined by the degeneracy of\ud the dual surface similar to the case for the Gauss map\ud of a flat surface in the Euclidean space.\ud We study singularities of these flat surfaces and\ud dualities of singularities