Sobolev $H^1$ Geometry of the Symplectomorphism Group
Differential Geometry
2017-10-10 v1
Abstract
For a closed symplectic manifold with compatible Riemannian metric we study the Sobolev geometry of the group of all diffeomorphisms on which preserve the symplectic structure. We show that, for sufficiently large , the metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the metric carries conjugate points via some simple examples.
Keywords
Cite
@article{arxiv.1710.02859,
title = {Sobolev $H^1$ Geometry of the Symplectomorphism Group},
author = {James Benn and Ali Suri},
journal= {arXiv preprint arXiv:1710.02859},
year = {2017}
}