Berezin quantization of homogeneous bounded domains

Loi, Andrea; Mossa, Roberto

doi:10.1007/s10711-012-9697-1

Cited by 42 publications

(52 citation statements)

References 27 publications

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“…Similar results were recently generalized by the first author and Mossa [34] to all bounded homogeneous (not necessarily symmetric) domains. The case of general homogeneous Kähler manifolds (not necessarily bounded domains) is still open.…”

Section: Balanced Metrics: the Compact And The Noncompact Casesupporting

confidence: 75%

Some remarks on the Kähler geometry of the Taub-NUT metrics

2011

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In this article, we investigate the balanced condition and the existence of an Engliš expansion for the Taub-NUT metrics on C 2 . Our first result shows that a Taub-NUT metric on C 2 is never balanced unless it is the flat metric. The second one shows that an Engliš expansion of the Rawnsley's function associated to a Taub-NUT metric always exists, while the coefficient a 3 of the expansion vanishes if and only if the Taub-NUT metric is indeed the flat one.

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Section: Balanced Metrics: the Compact And The Noncompact Casesupporting

confidence: 75%

Some remarks on the Kähler geometry of the Taub-NUT metrics

2011

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“…For the case of non-compact manifolds, Loi-Mossa in [28] have shown that a bounded homogeneous domain admits a regular quantization. For the nonhomogeneous setting, we give the existence of regular quantizations on some Hartogs domains in [6] and [18].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The regular quantizations of certain holomorphic bundles

Feng

2019

Ann Glob Anal Geom

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In this paper, we study the regular quantizations of Kähler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector bundles and their ball subbundles to be regular quantizations. Secondly, we obtain that some projective bundles over the Fano manifolds M admit regular quantizations if and only if M are biholomorphically isomorphism to the complex projective spaces. Finally, we obtain the balanced metrics on certain Hermitian holomorphic vector bundles and their ball subbundles over the Riemann sphere.

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“…Equation(20) extends to the noncompact setting the analogous equation proved in[4] for the compact case.…”

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confidence: 81%