Bianchi type III foliation of the de Sitter space (Q1309014)

The authors describe an example of a space-time foliated by homogeneous space-like hypersurfaces such that the shear tensor of the normal vector field to the foliation is non-zero, and yet the space-time is isotropic, in fact embeds isometrically as an open subset of the de Sitter space. The importance of this example is to show that the shear tensor does not give reliable information concerning the degree of isotropy of a space-time.