# On an Important Non-Riemannian Quantity in Finsler Geometry

Research paper by Chen Guangzu, Cheng Xinyue

Indexed on: 07 Jan '14Published on: 07 Jan '14Published in: Results in Mathematics

#### Abstract

In this paper, we study a non-Riemannian quantity $${\bar{{\bf E}}}$$-curvature. We prove that if F is a projectively flat Finsler metric of nonzero flag curvature, then it is Riemannian if and only if $${{\bar{\bf E}}}$$-curvature vanishes. Further, we characterize the Einstein-Douglas metrics with vanishing $${{\bar{\bf E}}}$$-curvature.