Harris, Adam

Paternain, Gabriel P

2008

We explore the relationship between contact forms on S³ defined by Finsler metrics on S² and the theory developed by H. Hofer, K.Wysocki and E. Zehnder (Hofer et al. Ann. Math. 148, 197–289, 1998; Ann. Math. 157, 125–255, 2003). We show that a Finsler metric on S² 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 S² with K = 1, thus complementing the results obtained in Harris and Wysocki (Trans. Am. Math. Soc., to appear).

Annals of Global Analysis and Geometry, 34(2), p. 115-134

1572-9060

0232-704X

https://hdl.handle.net/1959.11/2919

Springer Netherlands

Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders

Journal Article

Publication