de Sitter microuniverse associated to the electron

In the theory of classical electron developed by one of the authors, to such a particle a de Sitter microuniverse is associated. The internal dynamics of the particle (considered as pointlike) takes place in this universe. In connection to the model of electron deriving from the above-mentioned theory, some geometrical properties of the de Sitter universe are studied and in particular his geodesical representation on a manifold (Castelnuovo universe) for which the geodesics are straight lines. The present paper allows us to clarify the mutual connections between the « internal » and the « external » (macroscopical) dynamics of the electron and consequently a better understanding of the physical meaning of the theory.