Abstract:
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.
Keywords:Hermitian structure, para-Hermitian structure, integrable almost complex structure, radical of a multilinear form.
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