Ricci flat Kähler metrics on rank two complex symmetric spaces
Journal de l’École polytechnique - Mathématiques, Volume 6 (2019), pp. 163-201.

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.

Nous obtenons des métriques kählériennes Ricci plates sur les espaces symétriques complexes de rang 2 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.

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Accepted:
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DOI: 10.5802/jep.91
Classification: 53C25,  14J32,  14M27
Keywords: Calabi-Yau metric; asymptotically conical metric; complex symmetric space; wonderful compactification
Biquard, Olivier 1; Delcroix, Thibaut 2

1 Sorbonne Université and École Normale Supérieure, PSL University 45 rue d’Ulm, 75005 Paris, France
2 Université de Strasbourg, IRMA 7 rue René Descartes, 67000 Strasbourg, France
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     title = {Ricci flat {K\"ahler} metrics on rank~two~complex symmetric spaces},
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Biquard, Olivier; Delcroix, Thibaut. Ricci flat Kähler metrics on rank two complex symmetric spaces. Journal de l’École polytechnique - Mathématiques, Volume 6 (2019), pp. 163-201. doi : 10.5802/jep.91. http://www.numdam.org/articles/10.5802/jep.91/

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