射影平坦spray的射影Ricci曲率
PDF下载 (197)王 伟,李本伶.射影平坦spray的射影Ricci曲率[J].宁波大学学报(理工版),2021,34(4):79-85.DOI:
WANG Wei,LI Benling.Projective Ricci curvature of projective flat spray[J].Journal of Ningbo University(Natural Science & Engineering Edition),2021,34(4):79-85.DOI:
| Title: | Projective Ricci curvature of projective flat spray |
| 作者: | 王 伟, 李本伶 |
| Author(s): | WANG Wei, LI Benling |
| 关键词: | 射影平坦; Ricci曲率; Randers度量 |
| Keywords: | projective flat; Ricci curvature; Randers metrics |
| 分类号: | O186 |
| 文献标识码: | A |
| 摘要: | 研究了射影Ricci平坦的spray和度量, 首先讨论射影平坦spray在给定的体积元条件下何时满足射影Ricci曲率为0的条件. 在此基础上, 刻画出在常用的Busemann-Hausdorff体积元情形下, 射影平坦Randers度量的射影Ricci曲率, 并给出Ricci曲率为常数时该度量的具体构造. |
| Abstract: | In this paper, the projective Ricci flat spray and its metrics are studied in the most part. Firstly, we discuss the case in which the projective flat spray meets the condition that the projective Ricci curvature is 0 with the given volume element. On this basis, by using Busemann-Hausdorff volume element, the projective Ricci curvature of projective flat Randers metrics is described, and the concrete structure of such metrics is given provided that the Ricci curvature is constant. |
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| 备注/Memo: | 收稿日期: 2020－10－14. 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: 王伟（1997－）, 男, 湖北黄冈人, 在读硕士研究生, 主要研究方向: 微分几何. E-mail: wangwei2020nbu@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/ |
