[Groupes dʼisométries des métriques de Sasaki–Einstein]
In this short paper we prove a conjecture of Martelli–Sparks–Yau regarding the isometry group of a Sasaki–Einstein metric.
Soit une variété de Sasaki–Einstein et la variété affine sous-jacente à son cône de Kähler. Nous montrons que la composante neutre du sous-groupe compact maximal du groupe des automorphismes de coïncide avec la composante neutre du groupe des isométries holomorphes de .
Accepté le :
Publié le :
He, Weiyong 1
@article{CRMATH_2014__352_1_71_0,
author = {He, Weiyong},
title = {Isometry group of {Sasaki{\textendash}Einstein} metric},
journal = {Comptes Rendus. Math\'ematique},
pages = {71--73},
year = {2014},
publisher = {Elsevier},
volume = {352},
number = {1},
doi = {10.1016/j.crma.2013.10.037},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2013.10.037/}
}
TY - JOUR AU - He, Weiyong TI - Isometry group of Sasaki–Einstein metric JO - Comptes Rendus. Mathématique PY - 2014 SP - 71 EP - 73 VL - 352 IS - 1 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2013.10.037/ DO - 10.1016/j.crma.2013.10.037 LA - en ID - CRMATH_2014__352_1_71_0 ER -
He, Weiyong. Isometry group of Sasaki–Einstein metric. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 71-73. doi: 10.1016/j.crma.2013.10.037
[1] Uniqueness of Einstein–Kähler metrics modulo connected group actions, Sendai, 1985 (Adv. Stud. Pure Math.), Volume vol. 10, North-Holland, Amsterdam (1987), pp. 11-40
[2] A Brunn–Minkowski-type inequality for Fano manifolds and the Bando–Mabuchi uniqueness theorem | arXiv
[3] Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, USA, 2008 (614 p)
[4] Extremal Kähler metrics. II, Differential Geometry and Complex Analysis, Springer, Berlin, 1985, pp. 95-114
[5] Transverse Kähler geometry of Sasaki manifolds and toric Sasaki–Einstein manifolds, J. Differ. Geom., Volume 83 (2009), pp. 585-636
[6] Group actions and curvature, Invent. Math., Volume 23 (1974), pp. 31-48
[7] Frankel conjecture and Sasaki geometry | arXiv
[8] Sasaki–Einstein Manifolds and Volume Minimisation, Commun. Math. Phys., Volume 280 (2007), pp. 611-673
[9] Sur la structure du groupe dʼhomeomorphismes analytiques dʼune certaine variete kehlerienne, Nagoya Math. J., Volume 11 (1957), pp. 145-150 (in French)
[10] Chern–Hamiltonʼs conjecture and K-contactness, Houst. J. Math., Volume 21 (1995) no. 4, pp. 709-718
[11] Uniqueness of Kähler–Ricci solitons, Acta Math., Volume 184 (2000) no. 2, pp. 271-305
Cité par Sources :





