On Bochner Curvature Tensors in almost Hermitian Manifolds

[Ganchev Georgi T.; Ганчев Георги Т.]A curvature identity characterizing almost Hermitian manifolds with pointwise constant antiholomorphic sectional curvatures is found. An antiholomorphic operator on curvature tensor is introduced and the vector space of the transformed curvature tensors is considered. A decomposition of this space under the action of unitary group is given using as a base tensors of constant antiholomorphic sectional curvatures. Considering a conformal equivalence to manifolds with zero holomorphic sectional curvatures, zero antiholomorphic sectional curvatures and zero constant type, theorems on the geometric meaning, respectively of the generalized Bochner tensor, Bochner tensor and almost Hermitian manifolds of conformal type are proved