no. 5
Einstein metrics on rational homology 7-spheres
[Métriques d'Einstein sur les 7-sphères d'homologie rationnelle]
Boyer, Charles P.1 ; Galicki, Krzysztof1 ; Nakamaye, Michael1
1 University of New Mexico, Department of Mathematics and Statistics, Albuquerque NM 87131 (USA)
Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1569-1584.

Dans cet article nous démontrons l'existence de structures d'Einstein sasakiennes sur certaines 7-sphères d'homologie rationnelle, 2-connexes. Elle apparaissent comme étant les premiers exemples non réguliers de métriques d'Einstein sasakiennes sur les sphères d'homologie rationnelle, simplement connexes. Nous décrivons aussi brièvement les 7- sphères d'homologie rationnelle qui admettent des structures sasakiennes positives régulières.

In this paper we demonstrate the existence of Sasakian-Einstein structures on certain 2- connected rational homology 7-spheres. These appear to be the first non-regular examples of Sasakian-Einstein metrics on simply connected rational homology spheres. We also briefly describe the rational homology 7-spheres that admit regular positive Sasakian structures.

DOI : 10.5802/aif.1925
Classification : 53C25, 53C12
Keywords: Einstein metrics, sasakian structures, homology spheres
Mot clés : métriques d'Einstein, structures sasakiennes, sphères homologiques

Boyer, Charles P. 1 ; Galicki, Krzysztof 1 ; Nakamaye, Michael 1

1 University of New Mexico, Department of Mathematics and Statistics, Albuquerque NM 87131 (USA) 
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     title = {Einstein metrics on rational homology 7-spheres},
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     pages = {1569--1584},
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Boyer, Charles P.; Galicki, Krzysztof; Nakamaye, Michael. Einstein metrics on rational homology 7-spheres. Annales de l'Institut Fourier, Tome 52 (2002) no. 5, pp. 1569-1584. doi : 10.5802/aif.1925. https://aif.centre-mersenne.org/articles/10.5802/aif.1925/

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