p-symplectic and p-pluriclosed structures on solvmanifolds

Let $(M,J)$ be a n-dimensional complex manifold: a p-K\"ahler structure (resp. p-symplectic structure) on M is a real, closed $(p,p)$-transverse form Ω (resp. real, closed $2p$-form whose $(p,p)$-component is transverse). We give obstructions to the existence of such structures on compact complex manifolds. We provide several families of compact complex manifolds which admit both $(n-1)$-symplectic structures and special Hermitian metrics.