  A proposal is made for what may well be the most elementary Riemannian spaces
which are homogeneous but not isotropic. In other words: a proposal is made for
what may well be the nicest symmetric spaces beyond the real space forms, that
is, beyond the Riemannian spaces which are homogeneous and isotropic. The above
qualification of `'nicest symmetric spaces'' finds a justification in that,
together with the real space forms, these spaces are most natural with respect
to the importance in human vision of our ability to readily recognise conformal
things and in that these spaces are most natural with respect to what in Weyl's
view is symmetry in Riemannian geometry.
  Following his suggestion to remove the real space forms' isotropy condition,
the quasi space forms thus introduced do offer a metrical, local geometrical
solution to the geometrical space form problem as posed by Thurston in his 1979
Princeton Lecture Notes on `'The Geometry and Topology of 3-manifolds''.
Roughly speaking, quasi space forms are the Riemannian manifolds of dimension
greater than or equal to 3, which are not real space forms but which admit two
orthogonally complementary distributions such that at all points all the
2-planes that in the tangent spaces there are situated in a same position
relative to these distributions do have the same sectional curvatures.
