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Holomorphically projective mappings of compact semisymmetric manifolds. (English) Zbl 1228.53018
Summary: We consider holomorphically projective mappings from the compact semisymmetric spaces \(A_n\) onto (pseudo-) Kählerian spaces \(K_n\). We prove that in this case \(A_n\) is holomorphically projective flat and \(K_n\) is a space with constant holomorphic curvature. These results are generalizations of results by T. Sakaguchi, J. Mikeš, V. V. Domashev, N. S. Sinyukov, E. N. Sinyukova, and M. Škodová, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.
MSC:
53B20 Local Riemannian geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53B35 Local differential geometry of Hermitian and Kählerian structures
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