一类具有消失χ曲率的(α,β)-度量

麻翠玲; 张晓玲; 何勇

doi:10.13568/j.cnki.651094.651316.2021.04.09.0001

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一类具有消失χ曲率的(α,β)-度量

更新时间：2026-01-21

- 一类具有消失χ曲率的(α,β)-度量
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 39, Issue 3, Pages: 300-305(2022)
- 作者机构：
  
  1. 新疆大学数学与系统科学学院
  2. 新疆师范大学数学科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2021.04.09.0001
  CLC： O186.1
- Published：2022
- 稿件说明：
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[1]麻翠玲,张晓玲,何勇.一类具有消失χ曲率的(α,β)-度量[J].新疆大学学报(自然科学版)(中英文),2022,39(03):300-305.
[1]麻翠玲,张晓玲,何勇.一类具有消失χ曲率的(α,β)-度量[J].新疆大学学报(自然科学版)(中英文),2022,39(03):300-305. DOI： 10.13568/j.cnki.651094.651316.2021.04.09.0001.

DOI：10.13568/j.cnki.651094.651316.2021.04.09.0001.

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.

Abstract

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.

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references

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SHEN Z M.On some non-Riemannian quantities in Finsler geometry[J].Canad Math Bull,2013,56:184-193.

CHEN G Z,LIU L H.On Kropina metrics with non-Riemannian curvature properties[J].Differential Geometry and its Applications,2015,43:180-191.

CHENG X Y,YUAN M G.On conformally fat(α,β)-metrics with special curvature properties[J].Acta Mathematica Sinica,English Series,2015,31:879-892.

ZHU H M.On a class of Finsler metrics with special curvature properties[J].Balkan Journal of Geometry and its Applications,2018,23:97-108.

LI B L,SHEN Z M.Sprays of isotropic curvature[J].International Journal of Mathematics,2018,DOI:10.1142/S0129167X18500039.

CHENG X Y,SHEN Z M.A class of Finsler metrics with isotropic S-curvature[J].Israel Journal of Mathmatics,2009,169:317-340.

CHENG X Y,WANG H,WANG M F.(α,β)-metrics with relatively isotropic mean Landsberg curvature[J].Publicationes Mathematicae,2008,72:475-485.

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