1S. Janeczko Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland and Wydział Matematyki i Nauk Informacyjnych Politechnika Warszawska Pl. Politechniki 1 00-661 Warszawa, Poland 2Z. Jelonek Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland
Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 147-160
Let $(X , \omega _X)$ and $(Y, \omega _Y)$ be compact symplectic manifolds (resp. symplectic manifolds) of dimension $2n>2.$
Fix $ 0 s n$ (resp. $ 0 k\leq n$) and assume that a diffeomorphism
${\Phi } : X \to Y$ 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
${\Phi }$ is a conformal symplectomorphism, i.e., there is a constant $c\not =0$ such that
${ \Phi }^*\omega _Y=c\omega _X.$
Keywords:
omega omega compact symplectic manifolds resp symplectic manifolds dimension fix resp leq assume diffeomorphism phi maps s dimensional symplectic submanifolds symplectic submanifolds resp isotropic k dimensional tori isotropic tori prove cases phi conformal symplectomorphism there constant phi * omega omega
Affiliations des auteurs :
Stanisław Janeczko
1
;
Zbigniew Jelonek
2
1
S. Janeczko Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland and Wydział Matematyki i Nauk Informacyjnych Politechnika Warszawska Pl. Politechniki 1 00-661 Warszawa, Poland
2
Z. Jelonek Instytut Matematyczny PAN Śniadeckich 8 00-956 Warszawa, Poland
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Stanisław Janeczko; Zbigniew Jelonek. Characterization of diffeomorphisms
that are symplectomorphisms. Fundamenta Mathematicae, Tome 205 (2009) no. 2, pp. 147-160. doi: 10.4064/fm205-2-4
