Comptes Rendus
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

Guoqiang Wu1 ; Shijin Zhang2
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, Volume 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
Guoqiang Wu 1 ; Shijin Zhang 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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Guoqiang Wu; Shijin Zhang. Remarks on shrinking gradient Kähler–Ricci solitons with positive bisectional curvature. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 713-716. doi : 10.1016/j.crma.2016.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.010/

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

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

[3] B. Chow; P. Lu; B. Yang 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] O. Munteanu; J.P. Wang Positively curved shrinking Ricci solitons are compact | arXiv

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

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