Let and be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-4,
author = {Stanis\l aw Janeczko and Zbigniew Jelonek},
title = {Characterization of diffeomorphisms that are symplectomorphisms},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {147-160},
zbl = {1182.53074},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-4}
}
Stanisław Janeczko; Zbigniew Jelonek. Characterization of diffeomorphisms that are symplectomorphisms. Fundamenta Mathematicae, Tome 205 (2009) pp. 147-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm205-2-4/