Geodesic
Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties
Canadian journal of mathematics, Tome 77 (2025) no. 5, pp. 1611-1636

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DOI

Let G be a simply connected semisimple compact Lie group, let X be a simply connected compact Kähler manifold homogeneous under G, and let L be a negative holomorphic line bundle over X. We prove that all G-invariant Kähler metrics on the total space of L arise from the Calabi ansatz. Using this, we show that there exists a unique G-invariant scalar-flat Kähler metric in each G-invariant Kähler class of L. The G-invariant scalar-flat Kähler metrics are automatically asymptotically conical.
DOI : 10.4153/S0008414X24000464
Mots-clés : Canonical metrics, Calabi ansatz, invariant scalar-flat Kähler metrics, asymptotically conical Kähler metrics 
Yao, Qi. Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties. Canadian journal of mathematics, Tome 77 (2025) no. 5, pp. 1611-1636. doi: 10.4153/S0008414X24000464
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     author = {Yao, Qi},
     title = {Invariant scalar-flat {K\"ahler} metrics on line bundles over generalized flag varieties},
     journal = {Canadian journal of mathematics},
     pages = {1611--1636},
     year = {2025},
     volume = {77},
     number = {5},
     doi = {10.4153/S0008414X24000464},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X24000464/}
}
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