  In the context of upcoming large-scale structure surveys such as Euclid, it
is of prime importance to quantify the effect of peculiar velocities on
geometric probes. Hence the formalism to compute in redshift space the
geometrical and topological one-point statistics of mildly non-Gaussian 2D and
3D cosmic fields is developed. Leveraging the partial isotropy of the target
statistics, the Gram-Charlier expansion of the joint probability distribution
of the field and its derivatives is reformulated in terms of the corresponding
anisotropic variables. In particular, the cosmic non-linear evolution of the
Minkowski functionals, together with the statistics of extrema are investigated
in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian
redshift distortion correction is estimated for these geometric probes. In 3D,
gravitational perturbation theory is implemented in redshift space to predict
the cosmic evolution of all relevant Gram-Charlier coefficients. Applications
to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming
surveys is discussed. Such statistics are of interest for anisotropic fields
beyond cosmology.

Cosmology and Nongalactic Astrophysics