On m-Kropina Finsler Metrics of Scalar Flag Curvature

被引：0
作者：
Yang, Guojun [1 ]
机构：
[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2019年 / 74卷 / 01期
基金：
中国国家自然科学基金;
关键词：
m-Kropina metric; flag curvature; projective flatness;
D O I：
10.1007/s00025-018-0946-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a special class of singular Finsler metrics: m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We show that an m-Kropina metric (m-1) of scalar flag curvature must be locally Minkowskian in dimension n3. We characterize by some PDEs a Kropina metric (m=-1) which is respectively of scalar flag curvature and locally projectively flat in dimension n3, and obtain some principles and approaches of constructing non-trivial examples of Kropina metrics of scalar flag curvature.
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