On two curvature-driven problems in Riemann-Finsler geometry. (English) Zbl 1147.53018

Sabau, Sorin V. (ed.) et al., Finsler geometry, Sapporo 2005. In memory of Makoto Matsumoto. Proceedings of the 40th Finsler symposium on Finsler geometry, Sapporo, Japan, September 6–10, 2005. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-42-6/hbk). Advanced Studies in Pure Mathematics 48, 19-71 (2007).
A survey on tensor calculus on Finsler manifolds is given. Among the various topics which are discussed are Berwald connections, the Landsberg tensor and the Gauss-Bonnet type theorem by D. Bao and S. S. Chern. The two problems mentioned in the title are the existence of a Landsberg metric which is not of Berwald type and the study of the Ricci flow on Finsler manifolds.
For the entire collection see [Zbl 1130.53005].


53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)