[Sur l’existence et l’unicité des solitons de Kähler–Ricci -invariantes]
We use the momentum construction for -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.
Nous utilisons la construction des métriques kähleriennes -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.
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Keywords: Kähler geometry, steady solitons, $S^1$-invariance
Mots-clés : géométrie de kähleriennne, solitons, $S^1$-invariance
Schäfer, Johannes 1
CC-BY 4.0
@article{AFST_2023_6_32_1_15_0,
author = {Sch\"afer, Johannes},
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},
year = {2023},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 32},
number = {1},
doi = {10.5802/afst.1726},
language = {en},
url = {https://www.numdam.org/articles/10.5802/afst.1726/}
}
TY - JOUR AU - Schäfer, Johannes TI - Existence and uniqueness of $S^1$-invariant Kähler–Ricci solitons JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2023 SP - 15 EP - 53 VL - 32 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://www.numdam.org/articles/10.5802/afst.1726/ DO - 10.5802/afst.1726 LA - en ID - AFST_2023_6_32_1_15_0 ER -
%0 Journal Article %A Schäfer, Johannes %T Existence and uniqueness of $S^1$-invariant Kähler–Ricci solitons %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2023 %P 15-53 %V 32 %N 1 %I Université Paul Sabatier, Toulouse %U https://www.numdam.org/articles/10.5802/afst.1726/ %R 10.5802/afst.1726 %G en %F AFST_2023_6_32_1_15_0
Schäfer, Johannes. 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
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