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 (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.