一类具有消失χ曲率的(α,β)-度量  

A Class of(α,β)-Metrics with Vanishing χ Curvature

作　　者：麻翠玲 张晓玲[1] 何勇[2] MA Cuiling;ZHANG Xiaoling;HE Yong(School of Mathematics and Systems Sciences,Xinjiang University,Urumqi Xinjiang 830017,China;Department of Mathematics,Xinjiang Normal University,Urumqi Xinjiang 830053,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017 [2]新疆师范大学数学科学学院,新疆乌鲁木齐830053

出　　处：《新疆大学学报（自然科学版）（中英文）》2022年第3期300-305,共6页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金(11961061,11461064,11761069);新疆大学博士启动基金(BS130107).

摘　　要：在芬斯勒几何中,χ曲率是由S曲率定义的一个重要的非黎曼量.研究了一类具有消失χ曲率的(α,β)-度量.首先,给出了一类(α,β)-度量的χ曲率表达式;其次得到了其具有消失χ曲率的刻画方程;最后,构造了一系列具有消失χ曲率的(α,β)-度量.In Finsler geometry,χ curvature is a significant non-Riemannian quantity,which is defined by S curvature.In this paper,we studied a class of(α,β)-metrics with vanishing χ curvature.Firstly,we gave the formula of χ curvature for a class of(α,β)-metrics.Secondly,we obtained its characterized equations with vanishingχ curvature.In the end,we constructed a series of(α,β)-metrics with vanishing χ curvature.

关 键 词：(Α Β)-度量 S曲率 χ曲率 多项式(α β)-度量 

分 类 号：O186.14[理学—数学]