ON A NOTABLE CONNECTION IN FINSLER GEOMETRY
ON A NOTABLE CONNECTION IN FINSLER GEOMETRY
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DOI：
10.1142/9789812812834_0042
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发表时间：
1996-09
期刊：
影响因子：
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通讯作者：
D. Bao;S. Chern
中科院分区：
文献类型：
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作者：
D. Bao;S. Chern
本文探讨了Finsler几何中一种特殊联络的优点，它解决了等价问题。这个连接是无挠的，并且与诱导度量“几乎”相容。我们发展了测地线和雅可比场的微积分。我们还表明，弧长的第二个变化的表达式，当表示在这个连接和它的曲率张量，是形式上相同的黎曼几何。这一事实，然后影响一个简单的推广的概念，截面曲率，以及一些比较定理，芬斯勒几何。
This paper explores the merits of a special connection in Finsler geometry which solves the equivalence problem. This connection is torsionfree and 'almost' compatible with the induced metric. We develop the calculus of geodesics and Jacobi fields. We also show that the expression for the second variation of arc length, when expressed in terms of this connection and its curvature tensor, is formally identical to that in Riemannian geometry. This fact then effects a straightforward generalization of the concept of sectional curvature, as well as a number of comparison theorems, to Finsler geometry.