The Geodesic Flow
The Geodesic Flow
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测地线流
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
W. Klingenberg
中科院分区：
文献类型：
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作者：
W. Klingenberg
在这一章中，我们将介绍一个新的方面，一个封闭的测地线。在前几章中，闭测地线被认为是在所有闭曲线的空间中以某种性质（即是泛函的临界值）区分的闭曲线，而我们现在将把闭测地线（或者说是沿着闭测地线的切向量场）看作是黎曼流形的切丛上的测地线流中的周期轨道。
In this chapter we are going to introduce a new aspect of a closed geodesic. Whereas in the previous chapters a closed geodesic was considered as a closed curve distinguished in the space of all closed curves by a certain property (i.e. being a critical value of a functional), we are now going to view a closed geodesic (or rather the tangent vector field along a closed geodesic) as a periodic orbit in the geodesic flow on the tangent bundle of a Riemannian manifold.