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.
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.
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
@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}, 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 = {https://aif.centre-mersenne.org/articles/10.5802/aif.1925/} }
TY - JOUR AU - Boyer, Charles P. AU - Galicki, Krzysztof AU - Nakamaye, Michael TI - Einstein metrics on rational homology 7-spheres JO - Annales de l'Institut Fourier PY - 2002 SP - 1569 EP - 1584 VL - 52 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1925/ DO - 10.5802/aif.1925 LA - en ID - AIF_2002__52_5_1569_0 ER -
%0 Journal Article %A Boyer, Charles P. %A Galicki, Krzysztof %A Nakamaye, Michael %T Einstein metrics on rational homology 7-spheres %J Annales de l'Institut Fourier %D 2002 %P 1569-1584 %V 52 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1925/ %R 10.5802/aif.1925 %G en %F 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, Volume 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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