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 GR N with almost complex structure F i h 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 GK N and G K ‾ N it is impossible to obtain a generalization of the holomorphically projective curvature tensor. In the present paper we study the case when GK N and G K ‾ N have the same torsion in corresponding points. Such a mapping we call “equitorsion mapping”. We obtain quantities H P W θ ( θ = 1 , ⋯ , 5 ) , that are generalizations of the holomorphically projective tensor, i.e. they are invariants based on f . Among H P W θ only H P W 5 is a tensor. Using another five linearly independent curvature tensors, we can prove that there exist three holomorphically projective tensors. [ABSTRACT FROM AUTHOR]