具有常曲率的芬斯勒空间

西南师范大学学报(自然科学版)

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具有常曲率的芬斯勒空间

具有常曲率的芬斯勒空间[J]. 西南师范大学学报(自然科学版), 2005, 30(5).

引用本文:

具有常曲率的芬斯勒空间[J]. 西南师范大学学报(自然科学版), 2005, 30(5).

Two Kinds of Finsler Spaces with Constant Curvature[J]. Journal of Southwest China Normal University(Natural Science Edition), 2005, 30(5).

Citation:

Two Kinds of Finsler Spaces with Constant Curvature[J]. Journal of Southwest China Normal University(Natural Science Edition), 2005, 30(5).

摘要: 研究一类满足L:0+K(x,y)F2C=0的芬斯勒空间.证明了它一定具有常曲率,并得到一些有趣的相关结论,解决了下述著名定理的反问题:具有常曲率λ的芬斯勒空间一定满足L:0+λF2C=0.文章后半部分探讨了射影平坦的芬斯勒空间,得到它成为常曲率空间的一个条件.
- 数量曲率、常曲率、射影平坦
Abstract: In the present paper, the authors first study Finsler spaces satisfying L:0+K(x, y)F2 C=0, show that itmust be of constant curvature, and obtain some interesting conclusions. In fact, they solve a reverse problem of thefollowing well-known theorem: Finsler spaces of constant curvature λ must satisfy L:0 +λF2C=0. Then they focuson a projectively flat Finsler spaces, find a sufficient condition for it to be of constant curvature.
- scalar curvature .