Degenerate multilinear forms and Hermitian and para-Hermitian structures

We describe some method for obtaining families of complex and paracomplex structures on real manifolds by using degenerate skew-symmetric multilinear forms. To construct these structures, we employ a skew-symmetric form with nontrivial radical and obtain a family of almost complex structures on the six-dimensional sphere different from the Cayley structure and families of Hermitian and para-Hermitian structures on some six-dimensional manifolds.