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In this paper we consider holomorphically projective mappings from the compact semisymmetric spaces $A_n$ onto (pseudo-) Kählerian spaces ${\overline{K}}_n$. We proved that in this case space $A_n$ is holomorphically projective flat and ${\overline{K}}_n$ is space with constant holomorphic curvature. These results are the generalization of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian...

In this paper we find the metric in an explicit shape of special $2F$-flat Riemannian spaces $V_n$, i.e. spaces, which are $2F$-planar mapped on flat spaces. In this case it is supposed, that $F$ is the cubic structure: $F^3=I$.

In this paper we consider holomorphically projective mappings from the special generally recurrent equiaffine spaces $A_n$ onto (pseudo-) Kählerian spaces ${\overline{K}}_n$. We proved that these spaces $A_n$ do not admit nontrivial holomorphically projective mappings onto ${\overline{K}}_n$. These results are a generalization of results by T. Sakaguchi, J. Mikeš and V. V. Domashev, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.