Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2020, Vol. 49(1): 83-94
研究论文
关于广义${(\alpha,\beta)}$-度量的若干Ricci曲率性质
On Some Ricci Curvature Properties of the General ${(\alpha,\beta)}$-metrics

程新跃1,*, 吴莎莎2, 黄勤荣2
CHENG Xinyue1, WU Shasha2, HUANG Qinrong2

1. 重庆师范大学数学科学学院, 重庆, 401331;
2. 重庆理工大学理学院, 重庆, 400054
1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, P. R. China;
2. School of Sciences, Chongqing University of Technology, Chongqing, 400054, P. R. China

收稿日期: 2018-10-22
出版日期: 2020-03-25
2020, Vol. 49(1): 83-94
DOI: 10.11845/sxjz.2018088b


PDF
[355 KB]
38
下载
77
浏览

引用导出
0
    /   /   推荐

摘要 本文研究了广义($\alpha,\beta$)-度量的Ricci曲率和Ricci曲率张量.首先, 在一定条件下, 本文给出了强 Einstein广义($\alpha,\beta$)-度量的一个等价刻画.进一步, 得到了广义($\alpha,\beta$)-度量是Ricci-齐次Finsler度量的一个充分必要条件.
关键词 Finsler度量广义($\alpha,\beta$)-度量Ricci曲率Ricci曲率张量Einstein 度量Ricci-齐次度量    
Abstract:In this paper, we study the Ricci curvature and Ricci curvature tensor of the general ($\alpha,\beta$)-metrics. First, under certain conditions, we give an equivalent characterization of the strong Einstein general ($\alpha,\beta$)-metrics. Furthermore, we obtain a sufficient and necessary condition for a general ($\alpha,\beta$)-metric to be a Ricci-quadratic Finsler metric.
Key wordsFinsler metric    general ($\alpha,\beta$)-metric    Ricci curvature    Ricci curvature tensor    Einstein metric    Ricci-quadratic metric
PACS:  O186.14  
基金资助:国家自然科学基金(No. 11871126)和重庆师范大学科学研究基金 (No. 17XLB022).
通讯作者: E-mail:*chengxy@cqnu.edu.cn   
[1] Akbar-Zadeh, H., Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci. (5), 1988, 74(10): 281-322 (in French).
[2] Bácsó S., Cheng X.Y. and Shen Z.M., Curvature properties of $(\alpha,\beta)$-metrics, In: Finsler Geometry, Sapporo 2005---In Memory of Makoto Matsumoto (Sabau, S. and Shimada, H. eds.), Adv. Stud. Pure Math., Vol. 48, Tokyo: Math. Soc. Japan, 2007, 73-110.
[3] Bao, D. and Robles, C., Ricci and flag curvatures in Finsler geometry, In: A Sampler of Riemann-Finsler Geometry, MSRI Publications, Math. Sci. Res. Inst. Publ., Book 50, Cambridge: Cambridge Univ. Press, 2004, 197-259.
[4] Bao D., Robles C. and Shen Z.M., Zermelo navigation on Riemannian manifolds, J. Differential Geom., 2004, 66(3): 377-435.
[5] Cheng, X.Y. and Shen, Z.M., Randers metrics of scalar flag curvature, J. Aust. Math. Soc., 2009, 87(3): 359-370.
[6] Cheng, X.Y. and Shen, Z.M., Einstein Finsler metrics and Killing vector fields on Riemannian manifolds, Sci. China Math., 2017, 60(1): 83-98.
[7] Cheng X.Y., Shen Z.M. and Tian Y.F., A class of Einstein $(\alpha,\beta)$-metrics, Israel J. Math., 2012, 192(1): 221-249.
[8] Hu, Z.G. and Deng, S.Q., Ricci-quadratic homogeneous Randers spaces, Nonlinear Anal., 2013, 92: 130-137.
[9] Huang L.B.,Einstein Finsler metrics on $S^3$ with nonconstant flag curvature, Houston J. Math., 2011, 37(4): 1071-1086.
[10] Li, B.L. and Shen, Z.M., On Randers metrics of quadratic Riemann curvature, Internat. J. Math., 2009, 20(3): 369-376.
[11] Li, B.L. and Shen, Z.M., Ricci curvature tensor and non-Riemannian quantities, Canad. Math. Bull., 2015, 58(3): 530-537.
[12] Sadeghzadeh N.,On Finsler metrics of quadratic curvature, J. Geom. Phys., 2018, 132: 75-83.
[13] Shen Z.M.,On $R$-quadratic Finsler spaces, Publ. Math. Debrecen, 2001, 58(1/2): 263-274.
[14] Shen Z.M.,On some non-Riemannian quantities in Finsler geometry, Canad. Math. Bull., 2013, 56(1): 184-193.
[15] Shen, Z.M. and Yang, G.J., On square metrics of scalar flag curvature, Israel J. Math., 2018, 224(1): 159-188.
[16] Shen, Z.M. and Yu, C.T., On a class of Einstein Finsler metrics, Internat. J. Math., 2014, 25(4): 1450030, 18 pp.
[17] Xia Q.L.,On a class of Finsler metrics of scalar flag curvature, Results Math., 2017, 71(1/2): 483-507.
[18] Yu C.T.,Deformations and Hilbert's fourth problem, Math. Ann., 2016, 365(3/4): 1379-1408.
[19] Yu, C.T. and Zhu, H.M., On a new class of Finsler metrics, Differential Geom. Appl., 2011, 29(2): 244-254.
[20] Yu, C.T. and Zhu, H.M., Projectively flat general $(\alpha,\beta)$-metrics with constant flag curvature, J. Math. Anal. Appl., 2015, 429(2): 1222-1239.
[1] 陈亚力, 宋卫东. 具有相对迷向Landsberg曲率的球对称Finsler度量[J]. 数学进展, 2018, 47(1): 117-128.
[2] 张纪平, 魏献祝. 射影平坦的Landsberg度量[J]. 数学进展, 2016, 45(3): 449-454.
[3] 宋卫东,朱静勇. 一类常旗曲率为1的射影平坦Finsler度量[J]. 数学进展, 2013, 42(5): 731-735.
[4] 邓义华. 复乘积流形上Berwald度量与强Kähler-Finsler度量的构造(英)[J]. 数学进展, 2012, 41(6): 723-731.
[5] 程新跃. 关于射影平坦Finsler空间(英文)[J]. 数学进展, 2002, 31(4): 337-342.
[6] 詹华税. 关于H.Wu问题[J]. 数学进展, 2000, 29(4): 362-368.
Viewed
Full text


Abstract

Cited

  Discussed   
首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录


© 2015-2017 北京大学图书馆 .