XXVI International Fall Workshop on Geometry and Physics

Braga, 4-7 September 2017

The action of the group SO(3) in the Hilbert space of spin j H allows a principal fiber bundle structure, and split the tangent space in each point in two vectorial subspaces, the vectical and horizontal space, where the horizontal vectors are defined as the ortogonal vectors of the vertical ones with the FS metric. By the other hand, the Majorana’s stellar representation gives us a geometric view of H and its tangent bundle TH in terms of moving points on the sphere. In this representation, the vertical vectors have a clear interpretation, but the horizontal vectors don't. We expose some properties of the FS metric, the characteristics of the vertical vectors and a study of the horizontality condition in terms of the stellar representation.