The complete group of structural equations for a nearly Kahler manifold

In this thesis, we consider almost complex and almost Hermitian structures and their attached G-structures. It is proved that defining a complex structure on a real linear space is equivalent to decomposing its complexification into a direct sum of two complex conjugate subspaces that serve as proper subspaces of this complex structure. We prove that there exists an almost Hermitian structure on every almost complex manifold. We prove that setting an almost Hermitian structure on a smooth manifold is equivalent to setting a G-structure on this manifold with the structure group G=U(n) On the space of an attached G-structure, we obtain a complete group of structural equations and give fundamental identities for nearly Kahler manifolds.