期刊
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
卷 16, 期 8, 页码 1571-1616出版社
EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JEMS/470
关键词
Hamiltonian diffeomorphism; Hofer metric; coisotropic submanifold; symplectic rigidity; weightlessness
资金
- NSF [DMS-1105700]
In [Ch00], Chekanov showed that the Hofer norm on the Hamiltonian diffeomorphism group of a geometrically bounded symplectic manifold induces a nondegenerate metric on the orbit of any compact Lagrangian submanifold under the group. In this paper we consider the orbits of more general submanifolds. We show that, for the Chekanov Hofer pseudometric on the orbit of a closed submanifold to be a genuine metric, it is necessary for the submanifold to be coisotropic, and we show that this condition is sufficient under various additional geometric assumptions. At the other extreme, we show that the image of a generic closed embedding with any codimension larger than one is weightless, in the sense that the Chekanov Hofer pseudometric on its orbit vanishes identically. In particular this yields examples of submanifolds which have zero displacement energy but are not infinitesimally displaceable.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据