no. 7
Differential geometry
Remarks on shrinking gradient Kähler–Ricci solitons with positive bisectional curvature
[Remarques sur les solitons de Kähler–Ricci évanescents à courbure bisectionnelle positive]

Présenté par : the Editorial Board

Wu, Guoqiang1 ; Zhang, Shijin2
1 Department of Mathematics, East China Normal University, PR China
2 School of Mathematics and Systems Science, Beihang University, Beijing 100191, PR China
Comptes Rendus. Mathématique, Tome 354 (2016) no. 7, pp. 713-716.

Dans cette Note, en utilisant un argument de Munteanu et Wang, nous donnons une démonstration alternative du fait, déjà obtenu par Lei Ni, que les solitons de Kähler–Ricci évanescents de courbure bisectionelle positive sont compacts.

In this short note, using an argument by Munteanu and Wang, we provide an alternative proof of the fact first obtained by Lei Ni that shrinking gradient Kähler–Ricci solitons with positive bisectional curvature must be compact.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.04.010
Wu, Guoqiang 1 ; Zhang, Shijin 2

1 Department of Mathematics, East China Normal University, PR China
2 School of Mathematics and Systems Science, Beihang University, Beijing 100191, PR China 
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Wu, Guoqiang; Zhang, Shijin. Remarks on shrinking gradient Kähler–Ricci solitons with positive bisectional curvature. Comptes Rendus. Mathématique, Tome 354 (2016) no. 7, pp. 713-716. doi : 10.1016/j.crma.2016.04.010. http://www.numdam.org/articles/10.1016/j.crma.2016.04.010/

[1] Cao, H.D.; Zhou, D.T. On complete gradient shrinking Ricci solitons, J. Differ. Geom., Volume 85 (2010) no. 2, pp. 175-185

[2] Chow, B.; Chu, S.C.; Glickenstein, D.; Guenther, C.; Isenberg, J.; Ivey, T.; Knopf, D.; Lu, P.; Luo, F.; Ni, L. The Ricci Flow: Techniques and Applications. Part I. Geometric Aspects, Mathematical Surveys and Monographs, vol. 135, American Mathematical Society, Province, RI, USA, 2007

[3] Chow, B.; Lu, P.; Yang, B. Lower bounds for the scalar curvatures of noncompact gradient Ricci solitons, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011) no. 23–24, pp. 1265-1267

[4] Munteanu, O.; Wang, J.P. Positively curved shrinking Ricci solitons are compact | arXiv

[5] Ni, L. Ancient solutions to Kähler–Ricci flow, Math. Res. Lett., Volume 12 (2005) no. 5–6, pp. 633-653

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