Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature
arXiv:1602.06734 · doi:10.1016/j.crma.2016.04.001
Abstract
In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.
4 pages, accepted by CRMATHEMATIQUE