[Métriques kählériennes Ricci plates sur les espaces symétriques complexes de rang ]
Nous obtenons des métriques kählériennes Ricci plates sur les espaces symétriques complexes de rang à partir d’un modèle asymptotique explicite, dont la géométrie à l’infini s’interprète en termes de la compactification magnifique de l’espace symétrique. Dans le cas hermitien, on retrouve les métriques de Biquard-Gauduchon mais on produit aussi des métriques nouvelles.
We obtain Ricci flat Kähler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics of Biquard-Gauduchon in the Hermitian case and obtain in addition several new metrics.
Accepté le :
Publié le :
DOI : 10.5802/jep.91
Keywords: Calabi-Yau metric; asymptotically conical metric; complex symmetric space; wonderful compactification
Mot clés : Métrique de Calabi-Yau ; métrique asymptotiquement conique ; espace symétrique complexe ; compactification magnifique
Olivier Biquard 1 ; Thibaut Delcroix 2
CC-BY 4.0
@article{JEP_2019__6__163_0,
author = {Olivier Biquard and Thibaut Delcroix},
title = {Ricci flat {K\"ahler} metrics on rank~two~complex symmetric spaces},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {163--201},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.91},
zbl = {07033369},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.91/}
}
TY - JOUR AU - Olivier Biquard AU - Thibaut Delcroix TI - Ricci flat Kähler metrics on rank two complex symmetric spaces JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 163 EP - 201 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.91/ DO - 10.5802/jep.91 LA - en ID - JEP_2019__6__163_0 ER -
%0 Journal Article %A Olivier Biquard %A Thibaut Delcroix %T Ricci flat Kähler metrics on rank two complex symmetric spaces %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 163-201 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.91/ %R 10.5802/jep.91 %G en %F JEP_2019__6__163_0
Olivier Biquard; Thibaut Delcroix. Ricci flat Kähler metrics on rank two complex symmetric spaces. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 163-201. doi : 10.5802/jep.91. https://jep.centre-mersenne.org/articles/10.5802/jep.91/
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