Some invariants of holomorphically projective mappings of generalized Kählerian spaces

In the present paper a generalized Kählerian space is considered, as a generalized Riemannian space GRN with almost complex structure Fih that is covariantly constant with respect to the first and the second kind of covariant derivative. In the general case of a holomorphically projective mapping f of two non-symmetric generalized Kählerian spaces GKN and GK‾N it is impossible to obtain a generalization of the holomorphically projective curvature tensor. In the present paper we study the case when GKN and GK‾N have the same torsion in corresponding points. Such a mapping we call “equitorsion mapping”. We obtain quantities HPWθ(θ=1,⋯,5), that are generalizations of the holomorphically projective tensor, i.e. they are invariants based on f. Among HPWθ only HPW5 is a tensor. Using another five linearly independent curvature tensors, we can prove that there exist three holomorphically projective tensors.