Comptes Rendus
Analyse et géométrie complexes
Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 305-313.

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 ε-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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DOI : 10.5802/crmath.283
Classification : 32A25, 32Q15, 53C55

Enchao Bi 1 ; Zelin Hou 1

1 School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Canonical metrics on generalized {Hartogs} triangles},
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     doi = {10.5802/crmath.283},
     language = {en},
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Enchao Bi; Zelin Hou. Canonical metrics on generalized Hartogs triangles. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 305-313. doi : 10.5802/crmath.283. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.283/

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