Characterization of diffeomorphisms that are symplectomorphisms

Stanisław Janeczko, and Zbigniew Jelonek. "Characterization of diffeomorphisms that are symplectomorphisms." Fundamenta Mathematicae 205.2 (2009): 147-160. <http://eudml.org/doc/282824>.

@article{StanisławJaneczko2009,
abstract = {Let $(X,ω_X)$ and $(Y,ω_Y)$ 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 $Φ*ω_\{Y\} = cω_\{X\}$.},
author = {Stanisław Janeczko, Zbigniew Jelonek},
journal = {Fundamenta Mathematicae},
keywords = {symplectic submanifolds; isotropic tori; conformal symplectomorphism},
language = {eng},
number = {2},
pages = {147-160},
title = {Characterization of diffeomorphisms that are symplectomorphisms},
url = {http://eudml.org/doc/282824},
volume = {205},
year = {2009},
}

TY - JOUR
AU - Stanisław Janeczko
AU - Zbigniew Jelonek
TI - Characterization of diffeomorphisms that are symplectomorphisms
JO - Fundamenta Mathematicae
PY - 2009
VL - 205
IS - 2
SP - 147
EP - 160
AB - Let $(X,ω_X)$ and $(Y,ω_Y)$ 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 $Φ*ω_{Y} = cω_{X}$.
LA - eng
KW - symplectic submanifolds; isotropic tori; conformal symplectomorphism
UR - http://eudml.org/doc/282824
ER -