摘要
讨论了一类具有如下形式的Finsler度量F=α+εβ+kβ~2/α+k^2β~4/3α~3-k^3β~6/5α~5,其中α=(a_(ij)y^iy^j)^(1/2)是一个Riemann度量,β=b_iy^i是一个1-形式,ε和k≠0是常数,研究了这类度量的旗曲率性质,得到了F为局部射影平坦的充要条件.
A class of Finsler metrics in the following form
F=α＋εβ＋κβ^2/α＋κ^2β^4/3α^3-κ^3β^6/5α^5,
are discussed, where α=√αijy^iy^j is a Riemann metric,β=biy^j is a 1-form, ε and k ≠ 0 are constants. The properties of flag curvature for these metrics are studied, and the sufficient and necessary condition of locally projectively flat for F is obtained.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第6期1365-1370,共6页
Acta Mathematica Sinica：Chinese Series
关键词
射影平坦
(α
β)度量
常旗曲率
projectively flat
（α,β） metric
constant flag curvature
