| 关于射影Ricci曲率的比较定理与共形不变性 |
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| 引用本文： | 程新跃,李婷婷,殷丽.关于射影Ricci曲率的比较定理与共形不变性[J].西南农业大学学报,2019,41(2):52-59. |
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| 作者姓名： | 程新跃 李婷婷 殷丽 |
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| 作者单位： | 重庆师范大学数学科学学院;重庆新东方培训学校优能中学部 |
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| 基金项目： | 国家自然科学基金项目（11871126）；重庆师范大学科学研究基金项目（17XLB022）. |
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| 摘 要： | 主要研究了芬斯勒度量的射影Ricci曲率.首先,在一个完备的芬斯勒流形上,证明了关于芬斯勒度量的射影Ricci曲率的一个比较定理.其次,刻画了两个共形相关的芬斯勒度量的射影Ricci曲率的关系.在此基础上,证明了两个位似相关的芬斯勒度量的射影Ricci曲率是相等的.
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| 关 键 词： | 芬斯勒度量 射影Ricci曲率 Ricci曲率 S-曲率 共形相关 |
| 收稿时间： | 2018/1/8 0:00:00 |
On the Comparison Theorem and Conformal Invariance of a Projective Ricci Curvature |
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| CHENG Xin-yue,LI Ting-ting,YIN Li.On the Comparison Theorem and Conformal Invariance of a Projective Ricci Curvature[J].Journal of Southwest Agricultural University,2019,41(2):52-59. |
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| Authors: | CHENG Xin-yue LI Ting-ting YIN Li |
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| Institution: | 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;2. You Can Secondary School Department, Chongqing New Oriental Training School, Chongqing 400020, China |
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| Abstract: | In this paper, we study the projective Ricci curvature in Finsler geometry. First, we obtain that a comparison theorem on the projective Ricci curvature on a complete Finsler manifold. Then, we characterize the relations between two projective Ricci curvatures for two conformally related Finsler metrics on a manifold. On this basis, we prove that if two Finsler metrics are homothetically related, then their projective Ricci curvatures are equal. |
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| Keywords: | Finsler metric projective Ricci curvature Ricci curvature S-curvature conformally related |
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