2 problems

Let $(M,J, \omega)$ be a compact almost-Kähler manifold, where $J$ is an almost-complex structure and $\omega$ is its fundamental $2$-form. Let $\sigma$ be a smooth volume form on…

Let $M$ be a noncompact Einstein almost Kähler manifold, and suppose that every conformal vector field on $M$ is Killing. Rigidity Conjecture. Then $M$ must be isometric to complex…