Geometric meanings of curvatures in Finsler geometry (Q2722350)

In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this paper the author briefly discusses various curvatures and their geometric meanings from the metric geometry point of view, without going into the forest of tensors. The first four sections are devoted to the consideration of all quantities which vanish in Riemannian geometry. The fifth section is concerned with the Riemann curvature which was extended by Berwald (1926) to the Finslerian case. Then some well-known results due to S. Numata (1975), T. Okada (1983), H. Akbar-Zadeh (1988), R. Bryant (1996; 1997) and the present author on Finsler spaces of scalar curvature and of constant curvature are discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00020].