具有弱迷向数量曲率的Randers度量

程新跃, 龚妍廿

数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 1027-1036.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 1027-1036. DOI: 10.12386/A2021sxxb0085
论文

具有弱迷向数量曲率的Randers度量

    程新跃1, 龚妍廿2
作者信息 +

The Randers Metrics of Weakly Isotropic Scalar Curvature

    Xin Yue CHENG1, Yan Nian GONG2
Author information +
文章历史 +

摘要

本文研究了具有弱迷向数量曲率的Randers度量.证明了具有弱迷向数量曲率的Randers度量必定具有迷向S-曲率.进一步，证明了一个共形平坦且具有弱迷向数量曲率的非黎曼Randers度量一定是Minkowski度量.

Abstract

We study the Randers metrics of weakly isotropic scalar curvature. We prove that a Randers metric of weakly isotropic scalar curvature must be of isotropic S-curvature. Further, we prove that a conformally flat Randers metric of weakly isotropic scalar curvature is either Minkowskian or Riemannian.

关键词

芬斯勒几何 / Randers度量 / Ricci曲率张量 / 数量曲率 / S-曲率

Key words

Finsler geometry / Randers metric / Ricci curvature tensor / scalar curvature / S-curvature

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程新跃, 龚妍廿. 具有弱迷向数量曲率的Randers度量. 数学学报, 2021, 64(6): 1027-1036 https://doi.org/10.12386/A2021sxxb0085
Xin Yue CHENG, Yan Nian GONG. The Randers Metrics of Weakly Isotropic Scalar Curvature. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 1027-1036 https://doi.org/10.12386/A2021sxxb0085

参考文献

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基金

国家自然科学基金资助项目（11871126）；重庆师范大学科学基金资助项目（17XLB022）
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