| 关于射影平坦Finsler空间 |
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| 引用本文： | 程新跃.关于射影平坦Finsler空间[J].数学进展,2002,31(4):337-342. |
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| 作者姓名： | 程新跃 |
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| 作者单位： | 重庆工学院数学系,重庆,400050,中国 |
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| 基金项目： | the Science Foundation of Chongqing Education Committee. |
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| 摘 要： | 本文研究了射影平坦Finsler空间的几何量及其几何性质。证明了射影平坦Finsler空间的Ricci曲率可完全由射影因子简洁地刻画出来。同时还证明了，在射影平坦Finsler空间中，平均Berwald曲率S=0意味着Ricci曲率Ric是二次齐次的。此外，给出了一个射影平坦Finsler空间成为常曲率空间或局部Minkowski空间的充分条件。
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| 关 键 词： | Finsler度量 射影平坦Finsler空间 平均Berwald曲率 Ricci曲率 局部Minkowski空间 几何性质 |
| 修稿时间： | 1999年9月15日 |
On Projectively Flat Finsler Spaces |
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| Cheng Xinyue.On Projectively Flat Finsler Spaces[J].Advances in Mathematics,2002,31(4):337-342. |
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| Authors: | Cheng Xinyue |
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| Abstract: | In this paper,we study the geometric quantities and properties of projectively flat Finsler spaces. We prove that the Ricci curvature of a projectively flat Finsler space can be determined by the projective factor completely. Meanwhile, we show that the mean Berwald curvature S=0 implies that the Ricci curvature Ric is quadratic in projectively flat Finsler spaces. Moreover, we obtain some conditions that a projectively flat Finsler space is a space of constant curvature or is a locally Minkowski space. |
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| Keywords: | Finsler metric projectively flat Finsler space mean Berwald curvature Ricci curvature locally Minkowski space |
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