Symplectic cobordism of the projective spaces

Some geometric properties of projective spaces over the classical fields $R$, $C$, and $H$ are studied, which yield a new description of their symplectic cobordism modules. These results lead to new relations in the symplectic cobordism ring of a point. As an application, it is proved that $\theta_1\theta_i\theta_j=0$, where the $\theta_i$ are Ray's elements.