一类具有消失χ曲率的(α,β)-度量

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

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.