The complete group of structural equations for a nearly Kähler manifold

Abstract

We consider almost complex and almost Hermitian structures and their associated G - structures. It is proved that the definition of a complex structure on a real linear space is equivalent to the decomposition of its complexification into a direct sum of two complex conjugate subspaces that serve as proper subspaces of this complex structure. It is proved that on every almost complex manifold there exists an almost Hermitian structure.