Hodge-Riemann bilnear form on symplectic manifolds.

2010-10-15T16:32:49Z

Let $\omega$ a symplectic(may be Kahler) forms on $M^{2n}$. Then we have a symmetric bilnear two form on $H^2(M,\mathbb{R})$ given by

$ HR_\omega (\alpha,\beta) := < \alpha\beta[\omega]^{n-2}, [M] > $

for $\alpha, \beta \in H^2(M,\mathbb{R})$. (If $n=2$, then this form is just an intersection form.)

Is there any example of $(M^{2n}, \omega, \omega')$ such that $HR_\omega$ and $HR_\omega'$ have different set of eigenvalues? (with repetition)

Hodge-Riemann bilnear form on symplectic manifolds. - MathOverflow