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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.