  In this paper we propose a neurogeometrical model of the behaviour of cells
of the arm area of the primary motor cortex (M1). We mathematically express the
hypercolumnar organization of M1 discovered by Georgopoulos, as a fiber bundle,
as in classical sub-riemannian models of the visual cortex (Hoffmann, Petitot,
Citti-Sarti). On this structure, we consider the selective tuning of M1 neurons
of kinematic variables of positions and directions of movement. We then extend
this model to encode the notion of fragments of movements introduced by
Hatsopoulos. In our approach fragments are modelled as integral curves of
vector fields in a suitable sub-Riemannian space. These fragments are in good
agreements with movement decomposition from neural activity data. Here, we
recover these patterns through a spectral clustering algorithm in the
subriemannian structure we introduced, and compare our results with the
neurophysiological ones of Kadmon-Harpaz et al.
