Canonical metrics on generalized Hartogs triangles

Enchao Bi; Zelin Hou

doi:10.5802/crmath.283

Analyse et géométrie complexes

Canonical metrics on generalized Hartogs triangles

Enchao Bi ¹ ; Zelin Hou ¹

¹ School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R. China

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 305-313.

Résumé

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.

Reçu le : 2021-05-11
Révisé le : 2021-07-20
Accepté le : 2021-10-13
Publié le : 2022-04-26

DOI : 10.5802/crmath.283

Classification : 32A25, 32Q15, 53C55

Affiliations des auteurs :

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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     author = {Enchao Bi and Zelin Hou},
     title = {Canonical metrics on generalized {Hartogs} triangles},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {305--313},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     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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