Dynamically convex Finsler metrics and <Emphasis Type="Italic">J</Emphasis>-holomorphic embedding of asymptotic cylinders期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Dynamically convex Finsler metrics and <Emphasis Type="Italic">J</Emphasis>-holomorphic embedding of asymptotic cylinders

Authors:	Adam Harris Gabriel P Paternain

Institution:	(1) School of Mathematics, Statistics and Computer Sciences, University of New England, Armidale, NSW, 2351, Australia;(2) Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, CB3 0WB, England

Abstract:	We explore the relationship between contact forms on ${\mathbb{S}}^3$ defined by Finsler metrics on ${\mathbb{S}}^2$ and 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 on ${\mathbb{S}}^2$ with curvature K ≥ 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 construct J-holomorphic embeddings of cylinders asymptotic to Reeb orbits of contact structures arising from Finsler metrics on $\mathbb S^2$ with K = 1, thus complementing the results obtained in Harris and Wysocki (Trans. Am. Math. Soc., to appear).

Keywords:	J-holomorphic curves Finsler metric Contact forms Dynamic convexity
本文献已被 SpringerLink 等数据库收录！