no. 1
Differential geometry
Isometry group of Sasaki–Einstein metric
[Groupes dʼisométries des métriques de Sasaki–Einstein]

Présenté par : the Editorial Board

He, Weiyong1
1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 71-73.

Soit (M,g) une variété de Sasaki–Einstein et (X,J) 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 (X,J) coïncide avec la composante neutre du groupe des isométries holomorphes de (M,g).

In this short paper we prove a conjecture of Martelli–Sparks–Yau regarding the isometry group of a Sasaki–Einstein metric.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.10.037
He, Weiyong 1

1 Department of Mathematics, University of Oregon, Eugene, OR 97403, USA 
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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. http://www.numdam.org/articles/10.1016/j.crma.2013.10.037/

[1] Bando, S.; Mabuchi, T. 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] Berndtsson, B. A Brunn–Minkowski-type inequality for Fano manifolds and the Bando–Mabuchi uniqueness theorem | arXiv

[3] Boyer, C.; Galicki, K. Sasakian Geometry, Oxford Mathematical Monographs, Oxford University Press, USA, 2008 (614 p)

[4] Calabi, E. Extremal Kähler metrics. II, Differential Geometry and Complex Analysis, Springer, Berlin, 1985, pp. 95-114

[5] Futaki, A.; Ono, H.; Wang, G.-F. Transverse Kähler geometry of Sasaki manifolds and toric Sasaki–Einstein manifolds, J. Differ. Geom., Volume 83 (2009), pp. 585-636

[6] Grove, K.; Karcher, H.; Ruh, E. Group actions and curvature, Invent. Math., Volume 23 (1974), pp. 31-48

[7] He, W.-Y.; Sun, S. Frankel conjecture and Sasaki geometry | arXiv

[8] Martelli, D.; Sparks, J.; Yau, S.-T. Sasaki–Einstein Manifolds and Volume Minimisation, Commun. Math. Phys., Volume 280 (2007), pp. 611-673

[9] Matsushima, Y. Sur la structure du groupe dʼhomeomorphismes analytiques dʼune certaine variete kehlerienne, Nagoya Math. J., Volume 11 (1957), pp. 145-150 (in French)

[10] Rukimbira, P. Chern–Hamiltonʼs conjecture and K-contactness, Houst. J. Math., Volume 21 (1995) no. 4, pp. 709-718

[11] Tian, G.; Zhu, X.-H. Uniqueness of Kähler–Ricci solitons, Acta Math., Volume 184 (2000) no. 2, pp. 271-305

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