Two Kahler manifolds are called relatives if they admit a common submanifold with the same induced metrics. In this paper, we show that Hartogs domain over an irreducible bounded symmetric equipped Bergman metric is not relative to complex Euclidean space. This generalizes results in [5, 4] and novelty here kernel of necessarily Nash algebraic.

We show that the classical Bernstein polynomials BN (f)(x) on the interval [0, 1] (and their higher dimensional generalizations on the simplex Σm ⊂ R) may be expressed in terms of Bergman kernels for the Fubini-Study metric on CP: BN (f)(x) is obtained by applying the Toeplitz operator f(N−1Dθ) to the Fubini-Study Bergman kernels. The expression generalizes immediately to any toric Kähler varie...

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by Bergman. Our main result is that G is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that ω1-existentia...

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem. Superconnexion et noyaux de Bergman en famille Résumé. Nous annonçons des résultats sur le développement asymptotique du noyau de Bergman en famille. Let W,S be smooth compact complex manifolds. Let π : W → S be a holomorphic submersion with comp...

Inspired by mirror symmetry, we investigate some differential geometric aspects of the space Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory Weil-Petersson geometry stringy Kahler moduli space. A few basic examples are studied. In particular, identify our metric with Bergman Siegel modular variety in case self-product an elliptic curve.

Recently the authors characterized Fredholmn properties of Toeplitz operators on weighted Fock spaces when Laplacian weight function is bounded below and above. In present work extend their characterization to doubling with a subharmonic whose measure. The geometry induced by Bergman metric for much more complicated than that Euclidean used in all previous cases study Fredholmness, which leads ...

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.