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Maslov class rigidity for lagrangian submanifolds via hofer’s geometry, preprint 2008, arxiv:0808.1422.
| Content Provider | CiteSeerX |
|---|---|
| Author | Kerman, Ely Nil |
| Abstract | Abstract. 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. 1. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Lagrangian Submanifolds Hofer Geometry Maslov Class Rigidity Negative Sectional Curvature Convex Symplectic Manifold Maslov Class Displaceable Lagrangian Submanifolds Symplectic Manifold Negative Hofer Length Functional Periodic Orbit Product Manifold Large Class Geometric Hamiltonian Flow Main Result Establishes Upper Bound Closed Geodesic Minimal Maslov Number New Rigidity Result |
| Content Type | Text |
| Resource Type | Article |
