On geodesics of Finsler metrics via navigation problem
On geodesics of Finsler metrics via navigation problem
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DOI：
10.1090/s0002-9939-2011-10726-3
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发表时间：
2011-08
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影响因子：
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通讯作者：
Libing Huang;X. Mo
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文献类型：
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作者：
Libing Huang;X. Mo
本文研究了基于Zermelo导航的Finsler度量的测地线。我们给出了一个几何描述的Finsler度量的测地线从任何Finsler度量和任何位似字段的导航表示，推广了以前只知道在兰德斯度量的情况下，恒定的S-曲率的结果。作为它的应用，我们显式地给出了强凸域上Funk度量的测地线。
This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explicitly the geodesics of the Funk metric on a strongly convex domain.