Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders
Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders
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DOI：
10.1007/s10455-008-9111-2
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发表时间：
2007-01
影响因子：
0.7
通讯作者：
A. Harris;G. Paternain
中科院分区：
文献类型：
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作者：
A. Harris;G. Paternain
我们探讨了 Finsler 度量定义的接触形式与 H. Hofer、K. Wysocki 和 E. Zehnder 开发的理论之间的关系（Hofer 等人，Ann. Math.148, 197–289, 1998；Ann. Math.157, 125–255, 2003）。我们证明，曲率 K≥ 1 且所有长度 > π 的测地线环的芬斯勒度量是动态凸的，因此它具有两个或无限多个闭合测地线。我们还解释了如何显式构造由 Finsler 度量 onwithK=1 产生的接触结构 Reeb 轨道渐近的圆柱体 J 全纯嵌入，从而补充了 Harris 和 Wysocki（Trans. Am. Math. Soc.，即将出现）中获得的结果。
We explore the relationship between contact forms ondefined by Finsler metrics onand the theory developed by H. Hofer, K. Wysocki and E. Zehnder (Hofer etal. Ann. Math.148, 197–289, 1998; Ann. Math.157, 125–255, 2003). We show that a Finsler metric onwith curvatureK≥ 1 and with all geodesic loops of length > π is dynamically convex and hence it has either two or infinitely many closed geodesics. We also explain how to explicitly constructJ-holomorphic embeddings of cylinders asymptotic to Reeb orbits of contact structures arising from Finsler metrics onwithK= 1, thus complementing the results obtained in Harris and Wysocki (Trans. Am. Math. Soc., to appear).