Abstract:  Riemann-Finsler metrics on a manifold are

regular (not necessarily reversible) metrics. The flag

curvature is a natural extension of the sectional

curvature in Riemannian geometry. One of the

fundamental problems in Riemann-Finsler geometry is to

understand metrics of constant curvature. In this

talk, I am going to discuss some well-known metrics of

constant curvature (e.g. Hilbert metric, Funk metric,

etc.)  and some new examples.