  Adopting known data on positions and distances, we make use of the analytical
geometry and look for the plane that minimizes the distances of all galaxies to
it. A planar distribution is indeed found that, however, does not coincide with
the plane found by Sawa & Fujimoto 2005. Why? The second part of this study is
devoted to answer this question and to find a dynamical justification for the
planar distribution. To this aim, we apply the Hamilton Method (Minimum Action)
to investigate the dynamics of the two major system of the Local Group, Milky
Way and Andromeda, under the action of external forces exerted by nearby
galaxies or groups external to the Local Group. We find that the planar
istribution is fully compatible with the minimum action and that the external
force field is likely parallel to the plane. It pulls the galaxies of the Local
Group without altering their planar distribution. Special care is paid to
evaluate the robustness of this result. Conclusion: in this paper we have
examined the spatial distribution of galaxies in the Local Group. They are
confined to a plane that can be statistically and dynamically understood as the
result of the Minimum Action. The planar distribution seems to be stable for a
large fraction of the Hubble time. The external force field, that has likely
been constant over the same time interval, does not alter the planar
distribution as it is nearly parallel to it. Effects due to undetected halos of
sole Dark Matter are briefly discussed. They could be a point of uncertainty of
the present study.
