Canonical metrics on generalized Hartogs triangles

This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles. On the other hand, we calculate the explicit expression for Rawnsley’s $\varepsilon $-function, and th...

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Main Authors: Bi, Enchao, Hou, Zelin
Format: Article
Language:English
Published: Académie des sciences 2022-04-01
Series:Comptes Rendus. Mathématique
Online Access:https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/
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author Bi, Enchao
Hou, Zelin
author_facet Bi, Enchao
Hou, Zelin
author_sort Bi, Enchao
collection DOAJ
description This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles. On the other hand, we calculate the explicit expression for Rawnsley’s $\varepsilon $-function, and then we give the sufficient and necessary condition for the canonical metric to be balanced. As an application, we also find that there exist canonical metrics on generalized Hartogs triangles being both Kähler–Einstein and balanced.
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spelling doaj.art-e473e94625e94b0898d004a2e85fc80f2023-10-24T14:19:45ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692022-04-01360G430531310.5802/crmath.28310.5802/crmath.283Canonical metrics on generalized Hartogs trianglesBi, Enchao0Hou, Zelin1School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R. ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R. ChinaThis paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles. On the other hand, we calculate the explicit expression for Rawnsley’s $\varepsilon $-function, and then we give the sufficient and necessary condition for the canonical metric to be balanced. As an application, we also find that there exist canonical metrics on generalized Hartogs triangles being both Kähler–Einstein and balanced.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/
spellingShingle Bi, Enchao
Hou, Zelin
Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique
title Canonical metrics on generalized Hartogs triangles
title_full Canonical metrics on generalized Hartogs triangles
title_fullStr Canonical metrics on generalized Hartogs triangles
title_full_unstemmed Canonical metrics on generalized Hartogs triangles
title_short Canonical metrics on generalized Hartogs triangles
title_sort canonical metrics on generalized hartogs triangles
url https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/
work_keys_str_mv AT bienchao canonicalmetricsongeneralizedhartogstriangles
AT houzelin canonicalmetricsongeneralizedhartogstriangles