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Existence and uniqueness of S 1 -invariant Kähler–Ricci solitons
[Sur l’existence et l’unicité des solitons de Kähler–Ricci S 1 -invariantes]
Johannes Schäfer1
1 Universität Bonn, Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 1, pp. 15-53.

Nous utilisons la construction des métriques kähleriennes S 1 -invariantes de Hwang–Singer pour construire des nouveaux exemples de solitons de Kähler–Ricci. Nous montrons en outre que ces solitons sont uniques dans leur classe kählerienne, si le champ de vecteurs et les asymptotiques sont fixes.

We use the momentum construction for S 1 -invariant Kähler metrics as developed by Hwang–Singer to construct new examples of steady Kähler–Ricci solitons. We also prove that these solitons are unique in their Kähler class, provided the vector field and the asymptotic behaviour are fixed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1726
Classification : 53C55, 53C25, 53C21, 32L05
Keywords: Kähler geometry, steady solitons, $S^1$-invariance
Mot clés : géométrie de kähleriennne, solitons, $S^1$-invariance
Johannes Schäfer 1

1 Universität Bonn, Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Existence and uniqueness of $S^1$-invariant {K\"ahler{\textendash}Ricci} solitons},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {15--53},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 32},
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     year = {2023},
     doi = {10.5802/afst.1726},
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Johannes Schäfer. Existence and uniqueness of $S^1$-invariant Kähler–Ricci solitons. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 1, pp. 15-53. doi : 10.5802/afst.1726. https://afst.centre-mersenne.org/articles/10.5802/afst.1726/

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