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|Title:||Dynamically convex Finsler metrics and J-holomorphic embedding of asymptotic cylinders||Contributor(s):||Harris, Adam (author) ; Paternain, Gabriel P (author)||Publication Date:||2008||DOI:||10.1007/s10455-008-9111-2||Handle Link:||https://hdl.handle.net/1959.11/2919||Abstract:||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).||Publication Type:||Journal Article||Source of Publication:||Annals of Global Analysis and Geometry, 34(2), p. 115-134||Publisher:||Springer Netherlands||Place of Publication:||Amsterdam, The Netherlands||ISSN:||0232-704X
|Field of Research (FOR):||010111 Real and Complex Functions (incl Several Variables)||Socio-Economic Outcome Codes:||970101 Expanding Knowledge in the Mathematical Sciences||Peer Reviewed:||Yes||HERDC Category Description:||C1 Refereed Article in a Scholarly Journal||Statistics to Oct 2018:||Visitors: 124
|Appears in Collections:||Journal Article|
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