We prove that any compact simply connected manifold carrying a structure of Riemannian 3- or 4-symmetric space is formal in the sense of Sullivan. This result generalizes Sullivan's classical theorem on the formality of symmetric spaces, but the proof is of a different nature, since for generalized symmetric spaces techniques based on the Hodge theory do not work. We use the Thomas theory of minimal models of fibrations and the classification of 3- and 4-symmetric spaces.
@article{bwmeta1.element.bwnjournal-article-apmv64z1p17bwm,
author = {Anna Duma\'nska-Ma\l yszko and Zofia St\k epie\'n and Aleksy Tralle},
title = {Generalized symmetric spaces and minimal models},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {17-35},
zbl = {0856.53041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p17bwm}
}
Anna Dumańska-Małyszko; Zofia Stępień; Aleksy Tralle. Generalized symmetric spaces and minimal models. Annales Polonici Mathematici, Tome 63 (1996) pp. 17-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv64z1p17bwm/
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