On formality of generalized symmetric spaces

2001/06/30 by D. Kotschick, D. KOTSCHICK, S. Terzic +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology #math.AT #math.DG #msc:53C35 #msc:55P62 #msc:57T15 #msc:58A14

paper · pdf · doi:10.1017/s0305004102006540

published as Math. Proc. Cambridge Phil. Soc. 134 (2003), 491--505. · 18 pages; minor corrections; to appear in Mathematical Proceedings of the Cambridge Philosophical Society

arxiv created 2001/11/12 · openalex publication_date 2003/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that all generalized symmetric spaces of compact simple Lie groups are formal in the sense of Sullivan. Nevertheless, many of them, including all the non-symmetric flag manifolds, do not admit Riemannian metrics for which all products of harmonic forms are harmonic.

Cited by

• Hermitian geometrically formal manifolds

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