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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2022-04-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/ |
| _version_ | 1827785267023446016 |
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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. |
| first_indexed | 2024-03-11T16:16:45Z |
| format | Article |
| id | doaj.art-e473e94625e94b0898d004a2e85fc80f |
| institution | Directory Open Access Journal |
| issn | 1778-3569 |
| language | English |
| last_indexed | 2024-03-11T16:16:45Z |
| publishDate | 2022-04-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| 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 |