Sur les espaces de Finsler à courbures sectionnelles constantes

We give a characterization of the isotropic and constant sectional curvatures Finslerian manifolds. We determine necessary and sufficient conditions so that an isotropic Finslerian manifold is of constant sectional curvature K. In the case where the manifold is geodesically complete, we establish a classification of these manifolds according to the sign of K. We define three "axioms of planes" allowing to recognize if a Finslerian manifold is with constant sectional curvature in Berwald connection, or in Finslerian connection, or is Riemannian.