Generalized symmetric spaces and minimal models

Volume 64 / 1996

Anna Dumańska-Małyszko, Zofia Stępień, Aleksy Tralle Annales Polonici Mathematici 64 (1996), 17-35 DOI: 10.4064/ap-64-1-17-35


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.


  • Anna Dumańska-Małyszko
  • Zofia Stępień
  • Aleksy Tralle

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