不可度量化的射影平坦Spray的构造
PDF下载 (6610)娄艳文,李本伶.不可度量化的射影平坦Spray的构造[J].宁波大学学报(理工版),2020,33(6):103-106.DOI:
LOU Yanwen,LI Benling.Construction of non-metrizable projectively flat Spray[J].Journal of Ningbo University(Natural Science & Engineering Edition),2020,33(6):103-106.DOI:
| Title: | Construction of non-metrizable projectively flat Spray |
| 作者: | 娄艳文, 李本伶 |
| Author(s): | LOU Yanwen, LI Benling |
| 关键词: | Finsler度量; 射影平坦; 测地系数 |
| Keywords: | Spray; Finsler metric; projectively flat; geodesic coefficient |
| 分类号: | O186 |
| 文献标识码: | A |
| 摘要: | 刻画射影平坦Finsler度量是著名的Hilbert第四问题正则性情形, 且任意一个Finsler度量可以通过它的测地线方程诱导一个Spray, 因此研究射影平坦Spray的可度量化问题令人关注. 本文研究一类射影平坦Spray的可度量化问题, 通过欧氏度量和内积的线性组合, 构造两类射影平坦Spray; 其次利用反证法和具有迷向曲率Spray的定义, 证明以上两类Spray均不由任意Finsler度量诱导, 且不具有迷向曲率. |
| Abstract: | The regularity of Hilbert’s Fourth Problem concerns characterization of the projectively flat Finsler metric, and every Finsler metric induces a spray by its geodesic formula. This arouses attention to study the measurable problems of projectively flat spray. In this paper, we study the measurable problems of a class of projectively flat sprays, and construct two groups of projectively flat sprays by the linear combination of Euclidean metric and inner product. Next, using the proofs by contradiction and the definition of isotropic curvature for spray, it is proved that the above sprays are not induced by any Finsler metric and they are not of isotropic curvature. |
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| 备注/Memo: | 收稿日期:2020-05-12.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（R18A010002）. 第一作者:娄艳文（1992－）,女,河南新乡人,在读硕士研究生,主要研究方向:微分几何.E-mail:louyanwennbu@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、Finsler几何.E-mail:libenling@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
