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| Home > Articles > Published articles > Homogeneous contact compact manifolds and homogeneous symplectic manifolds |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 1980 |
| Abstract: | A homogeneous contact compact manifold can be considered as the total space of a principal circle bundle over a simply connected homogeneous symplectic manifold whose fundamental form determines an integral cohomology class. A similar result but assuming the contact manifold to be simply connected was given by Boothby and Wang. The proof we give here is independent of that of Boothby and Wang. We also prove that if a Lie group acts transitivelly on a simplectic manifold of integral class by diffeomorphism of the symplectic structure, there is a Lie group acting transitivelly on the total space of the bundle obtained from the symplectic form (Kobayashi's method) by diffeomorphisms of the contact structure. (The contact form is the correspondent connection form). |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Published in: | Publicacions de la Secció de Matemàtiques, V. 21 (1980) p. 25-27, ISSN 0210-2978 |
