Einstein metrics on rational homology 7-spheres
[Métriques d'Einstein sur les 7-sphères d'homologie rationnelle]
Boyer, Charles P. ; Galicki, Krzysztof ; Nakamaye, Michael
Annales de l'Institut Fourier, Tome 52 (2002), p. 1569-1584 / Harvested from Numdam
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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.

Publié le : 2002-01-01
DOI : https://doi.org/10.5802/aif.1925
Classification:  53C25,  53C12
Mots clés: métriques d'Einstein, structures sasakiennes, sphères homologiques 
@article{AIF_2002__52_5_1569_0,
     author = {Boyer, Charles P. and Galicki, Krzysztof and Nakamaye, Michael},
     title = {Einstein metrics on rational homology 7-spheres},
     journal = {Annales de l'Institut Fourier},
     volume = {52},
     year = {2002},
     pages = {1569-1584},
     doi = {10.5802/aif.1925},
     zbl = {1023.53029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2002__52_5_1569_0}
}

Boyer, Charles P.; Galicki, Krzysztof; Nakamaye, Michael. Einstein metrics on rational homology 7-spheres. Annales de l'Institut Fourier, Tome 52 (2002) pp. 1569-1584. doi : 10.5802/aif.1925. http://gdmltest.u-ga.fr/item/AIF_2002__52_5_1569_0/

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