A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY*
A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY*
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DOI：
10.1017/s0017089512000225
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发表时间：
2012-03
影响因子：
0.5
通讯作者：
X. Mo;Z. Shen;Huaifu Liu
中科院分区：
文献类型：
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作者：
X. Mo;Z. Shen;Huaifu Liu
摘要本文研究了由黎曼曲率定义的一个新的芬斯勒量Ĉ。对于维数n = 3的芬斯勒流形，我们证明了新的芬斯勒量是非黎曼量。然后研究了标量曲率的芬斯勒度量。我们发现Ĉ-curvature与旗子曲率和h曲率密切相关。我们证明Ĉ-curvature给出了芬斯勒度规弱各向同性标志曲率失效的一个测度。我们还给出了Najafi-Shen-Tayebi定理的一个简单证明。
Abstract In this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.