  Banyaga has shown that the group of symplectomorphisms Symp(N) of a compact
symplectic manifold (N,w) determines the symplectic structure. This motivates
the study of the homotopy properties of Symp(N). Gromov has shown that the
group of symplectomorphisms of N is homotopic to SO(3)\times SO(3) when N is
the product of two spheres endowed with the standard symplectic form. This
result generalizes the study of the homotopy type of the group of
diffeomorphisms of closed surfaces, by replacing the space of complex
structures by pseudo-complex structures adapted to w. A complex structure on a
surface induces on it a projective structure, the purpose of this paper is to
study the action of Symp(N) on homogeneous structures defined on N, and to
deduce homotopy properties of Symp(N).
