In this paper we work out the deformations of some flag manifolds and
of complex Minkowski space viewed as an affine big cell inside G(2,4).
All the deformations come in tandem with a coaction of the appropriat
e quantum group. In the case of the Minkowski space this allows us to
define the quantum conformal group. We also give two involutions on th
e quantum complex Minkowski space, that respectively define the real M
inkowski space and the real euclidean space. We also compute the quant
um De Rham complex for both real (complex) Minkowski and euclidean spa
ce.