CHARACTERIZATION AND STRUCTURE OF FINSLER-SPACES WITH CONSTANT FLAG CURVATURE

The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved that a Finsle r space has constant flag curvature 1 (resp. 0) if and only if the Ric ci curvature along the Hilbert form on the projective sphere bundle at tains identically its maximum (resp. Ricci scaler). The horizontal dis tribution H of this bundle is integrable if and only if M has zero fla g curvature. When a Finsler space has CFC, Hilbert form's orthogonal c omplement in the horizontal distribution is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and its first normal space is vertical.