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We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains for admissible weights .
We study the geometry of the second fundamental form of a Cauchy-Riemann submanifold of a Kaehlerian Finsler space M2n; any totally-real submanifold of M2n with v-flat normal connection is shown to be a Berwald-Cartan space.
We classify generic Cauchy-Riemann submanifolds (of a Kaehlerian manifold) whose fundamental form is preserved by any local geodesic symmetry.
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....
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