A Note on the Complete Kähler–Einstein Metrics of Disk Bundles Over Compact Homogeneous Kähler Manifolds
In this article, we focus on the explicit description of the Kähler–Einstein metric on the disk bundle over some simply connected compact homogeneous Kähler manifolds. More precisely, we consider a strictly pseudoconvex domain in a Hermitian line bundle, which is the disk bundle of the γ -tensor pow...
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| Veröffentlicht in: | The Journal of geometric analysis 2023-09, Vol.33 (9), Article 291 |
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| creator | Hao, Yihong Wang, An Zhang, Liyou |
| description | In this article, we focus on the explicit description of the Kähler–Einstein metric on the disk bundle over some simply connected compact homogeneous Kähler manifolds. More precisely, we consider a strictly pseudoconvex domain in a Hermitian line bundle, which is the disk bundle of the
γ
-tensor power of the negative canonical bundle over any compact homogeneous Kähler manifold. We obtained a necessary and sufficient condition for the existence of the Kähler–Einstein metric on such disk bundle, which generalized a recent proposition by Ebenfelt, Xiao and Xu. As an application, we study the explicit solution of the Monge–Ampère equation on the disk bundles over the complex flag manifolds of classical type. |
| doi_str_mv | 10.1007/s12220-023-01355-1 |
| format | Article |
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γ
-tensor power of the negative canonical bundle over any compact homogeneous Kähler manifold. We obtained a necessary and sufficient condition for the existence of the Kähler–Einstein metric on such disk bundle, which generalized a recent proposition by Ebenfelt, Xiao and Xu. As an application, we study the explicit solution of the Monge–Ampère equation on the disk bundles over the complex flag manifolds of classical type.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-023-01355-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Manifolds ; Mathematics ; Mathematics and Statistics ; Tensors</subject><ispartof>The Journal of geometric analysis, 2023-09, Vol.33 (9), Article 291</ispartof><rights>Mathematica Josephina, Inc. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-893eaf0b087b38a592cdc4bfa593e9c98a500bc6784c0e05754f53b8aa4eb62a3</cites><orcidid>0000-0002-3217-1950</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12220-023-01355-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-023-01355-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,782,786,27931,27932,41495,42564,51326</link.rule.ids></links><search><creatorcontrib>Hao, Yihong</creatorcontrib><creatorcontrib>Wang, An</creatorcontrib><creatorcontrib>Zhang, Liyou</creatorcontrib><title>A Note on the Complete Kähler–Einstein Metrics of Disk Bundles Over Compact Homogeneous Kähler Manifolds</title><title>The Journal of geometric analysis</title><addtitle>J Geom Anal</addtitle><description>In this article, we focus on the explicit description of the Kähler–Einstein metric on the disk bundle over some simply connected compact homogeneous Kähler manifolds. More precisely, we consider a strictly pseudoconvex domain in a Hermitian line bundle, which is the disk bundle of the
γ
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γ
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| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Manifolds Mathematics Mathematics and Statistics Tensors |
| title | A Note on the Complete Kähler–Einstein Metrics of Disk Bundles Over Compact Homogeneous Kähler Manifolds |
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