一类爱因斯坦Finsler度量的若干性质研究
PDF下载 (307)王利平,李本伶.一类爱因斯坦Finsler度量的若干性质研究[J].宁波大学学报(理工版),2019,32(4):68-72.DOI:
WANG Liping,LI Benling.On some properties of a class of Einstein Finsler metrics[J].Journal of Ningbo University(Natural Science & Engineering Edition),2019,32(4):68-72.DOI:
| Title: | On some properties of a class of Einstein Finsler metrics |
| 作者: | 王利平, 李本伶 |
| Author(s): | WANG Liping, LI Benling |
| 关键词: | 广义 -度量; Ricci曲率; 爱因斯坦度量; 弱爱因斯坦度量; Ricci平坦度量 |
| Keywords: | general -metric; Ricci curvature; Einstein metric; weakly Einstein metric; Ricci-flat metric |
| 分类号: | O186 |
| 文献标识码: | A |
| 摘要: | 爱因斯坦度量是Ricci曲率常数的度量以及比爱因斯坦度量更一般的弱爱因斯坦度量, 在理论物理中有重要的意义. 本文研究一类称为广义 -度量的Finsler度量, 首先得到广义 -度量 在共形条件下的Ricci曲率; 其次证明当 是弱爱因斯坦度量, 且 是关于 的二次多项式时, F必定是Ricci平坦爱因斯坦Finsler度量; 最后根据Ricci平坦Finsler度量的定义直接得出F是Ricci平坦Finsler度量的等价方程. |
| Abstract: | Einstein metric is a metric of constant Ricci curvature, and there is a more general one than Einstein metric which is called weakly Einstein metric. They bear important significance in theoretical physics. In this paper, we study a class of Finsler metrics called general -metrics. Firstly, we obtain the Ricci curvature of general -metric under the condition that is conformal with respect to . Secondly, when F is a weakly Einstein metric and a polynomial function of 2 degree with respect to s, we reach the conclusion that F is a Ricci-flat Finsler metric. Finally, the equivalent equation of the Ricci-flat Finsler metric is constructed based on the definition of the Ricci-flat Finsler metric. |
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| 备注/Memo: | 收稿日期: 2019－02－19. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 国家自然科学基金（11371209）; 浙江省自然科学基金（LR18A010002）.第一作者: 王利平（1992－）, 女, 安徽阜阳人, 在读硕士研究生, 主要研究方向: 微分几何. E-mail: wlpxwz341@163.com*通信作者: 李本伶（1979－）, 女, 浙江宁波人, 教授, 主要研究方向: 微分几何. E-mail: libenling@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
