Geodesic
Rigidity of Hamiltonian Actions
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 277-290

Voir la notice de l'article provenant de la source Cambridge

DOI

This paper studies the following question: Given an ${\omega }'$ -symplectic action of a Lie group on a manifold $M$ which coincides, as a smooth action, with a Hamiltonian $\omega$ -action, when is this action a Hamiltonian ${\omega }'$ -action? Using a result of Morse-Bott theory presented in Section 2, we show in Section 3 of this paper that such an action is in fact a Hamiltonian ${\omega }'$ -action, provided that $M$ is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.
DOI : 10.4153/CMB-2003-028-7
Mots-clés : 53D05, 37J25 
Rochon, Frédéric. Rigidity of Hamiltonian Actions. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 277-290. doi: 10.4153/CMB-2003-028-7
@article{10_4153_CMB_2003_028_7,
     author = {Rochon, Fr\'ed\'eric},
     title = {Rigidity of {Hamiltonian} {Actions}},
     journal = {Canadian mathematical bulletin},
     pages = {277--290},
     year = {2003},
     volume = {46},
     number = {2},
     doi = {10.4153/CMB-2003-028-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-028-7/}
}
TY  - JOUR
AU  - Rochon, Frédéric
TI  - Rigidity of Hamiltonian Actions
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 277
EP  - 290
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-028-7/
DO  - 10.4153/CMB-2003-028-7
ID  - 10_4153_CMB_2003_028_7
ER  - 
%0 Journal Article
%A Rochon, Frédéric
%T Rigidity of Hamiltonian Actions
%J Canadian mathematical bulletin
%D 2003
%P 277-290
%V 46
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-028-7/
%R 10.4153/CMB-2003-028-7
%F 10_4153_CMB_2003_028_7

Cité par Sources :