A closed 2-form

Question

Let $(M,\omega, J)$ be a Kaehler manifold with Levi-Civita connection $\nabla$ and Riemann curvature $R_{\nabla}$. I define a closed 2-form $\tilde{\omega}$:

$$\tilde{\omega}(X,Y)=\sum_{i=1}^n \omega (R_{\nabla}(X,Y) e_i, e_i)$$

Is the closed 2-form $\tilde{\omega}$ a symplectic form?