Einstein metrics on rational homology 7-spheres

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

doi:10.5802/aif.1925

Einstein metrics on rational homology 7-spheres
[Métriques d'Einstein sur les 7-sphères d'homologie rationnelle]

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

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.

Résumé
Abstract

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.

Zbl

DOI : 10.5802/aif.1925

Classification : 53C25, 53C12
Keywords: Einstein metrics, sasakian structures, homology spheres
Mot clés : métriques d'Einstein, structures sasakiennes, sphères homologiques

Affiliations des auteurs :

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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     author = {Boyer, Charles P. and Galicki, Krzysztof and Nakamaye, Michael},
     title = {Einstein metrics on rational homology 7-spheres},
     journal = {Annales de l'Institut Fourier},
     pages = {1569--1584},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {52},
     number = {5},
     year = {2002},
     doi = {10.5802/aif.1925},
     zbl = {1023.53029},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1925/}
}

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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. http://www.numdam.org/articles/10.5802/aif.1925/

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