Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry

Autor:	Kerman, Ely, Sirikci, Nil I.
Rok vydání:	2008
Předmět:	Mathematics - Symplectic Geometry Mathematics - Differential Geometry 53d12 (Primary) 53D40 37J45 (Secondary)
Druh dokumentu:	Working Paper
Popis:	In this work, we establish new rigidity results for the Maslov class of Lagrangian submanifolds in large classes of closed and convex symplectic manifolds. Our main result establishes upper bounds for the minimal Maslov number of displaceable Lagrangian submanifolds which are product manifolds whose factors each admit a metric of negative sectional curvature. Such Lagrangian submanifolds exist in every symplectic manifold of dimension greater than six or equal to four. The proof utilizes the relations between closed geodesics on the Lagrangian, the periodic orbits of geometric Hamiltonian flows supported near the Lagrangian, and the length minimizing properties of these flows with respect to the negative Hofer length functional. Comment: 34 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0808.1422 Zobrazit plný text záznamu View this record from Arxiv