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We establish an inversion formula for the M. M. Djrbashian A. H. Karapetyan integral transform (cf. [6]) on the Siegel domain , . We build a family of Kähler metrics of constant holomorphic curvature whose potentials are the -Bergman kernels, α > -1, (in the sense of Z. Pasternak-Winiarski [20] of . We build an anti-holomorphic embedding of in the complex projective Hilbert space and study (in connection with work by A. Odzijewicz [18] the corresponding transition probability amplitudes....
It is proved that there exists a non-semisymmetric pseudosymmetric Kähler manifold of dimension 4.
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