| 射影Ricci平坦的Kropina度量 |
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| 引用本文： | 程新跃,马小玉,沈玉玲. 射影Ricci平坦的Kropina度量[J]. 数学杂志, 2017, 37(4): 705-713 |
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| 作者姓名： | 程新跃 马小玉 沈玉玲 |
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| 作者单位： | 重庆理工大学数学与统计学院, 重庆 400054,重庆理工大学数学与统计学院, 重庆 400054,重庆理工大学数学与统计学院, 重庆 400054 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (11371386) and the European Union''s Seventh Framework Programme (FP7/2007-2013) under grant agreement (317721). |
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| 摘 要： | 本文研究和刻画了射影Ricci平坦的Kropina度量.利用Kropina度量的S-曲率和Ricci曲率的公式，得到了Kropina度量的射影Ricci曲率公式.在此基础上得到了Kropina度量是射影Ricci平坦度量的充分必要条件.进一步，作为自然的应用，本文研究和刻画了由一个黎曼度量和一个具有常数长度的Killing 1-形式定义的射影Ricci平坦的Kropina度量，也刻画了具有迷向S-曲率的射影Ricci平坦的Kropina度量.在这种情形下，Kropina度量是Ricci平坦度量.
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| 关 键 词： | 芬斯勒度量 Kropina度量 Ricci曲率 S-曲率 射影Ricci曲率 |
| 收稿时间： | 2015-07-16 |
| 修稿时间： | 2015-11-09 |
ON PROJECTIVE RICCI FLAT KROPINA METRICS |
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| CHENG Xin-yue,MA Xiao-yu and SHEN Yu-ling. ON PROJECTIVE RICCI FLAT KROPINA METRICS[J]. Journal of Mathematics, 2017, 37(4): 705-713 |
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| Authors: | CHENG Xin-yue MA Xiao-yu SHEN Yu-ling |
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| Affiliation: | School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China,School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China and School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China |
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| Abstract: | In this paper, we study and characterize projective Ricci flat Kropina metrics. By using the formulas of S-curvature and Ricci curvature for Kropina metrics, we obtain the formula of the projective Ricci curvature for Kropina metrics. Based on this, we obtain the necessary and su-cient conditions for Kropina metrics to be projective Ricci flat metrics. Further, as a natural application, we study and characterize projective Ricci flat Kropina metrics deflned by a Riemannian metric and a Killing 1-form of constant length. We also characterize projective Ricci flat Kropina metrics with isotropic S-curvature. In this case, the Kropina metrics are Ricci flat metrics. |
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| Keywords: | Finsler metric Kropina metrics Ricci curvature S-curvature projective Ricci curvature |
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