On formality of generalized symmetric spaces

D. KOTSCHICK; S. TERZIĆ

doi:10.1017/S0305004102006540

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.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Nagy, Paul-Andi 2006. On length and product of harmonic forms in Kähler geometry. Mathematische Zeitschrift, Vol. 254, Issue. 1, p. 199.

Ornea, Liviu and Pilca, Mihaela 2011. Remarks on the product of harmonic forms. Pacific Journal of Mathematics, Vol. 250, Issue. 2, p. 353.

Calvaruso, Giovanni 2011. Symplectic, complex and Kähler structures on four-dimensional generalized symmetric spaces. Differential Geometry and its Applications, Vol. 29, Issue. 6, p. 758.

Kotschick, Dieter and Terzić, Svjetlana 2011. Geometric formality of homogeneous spaces and of biquotients. Pacific Journal of Mathematics, Vol. 249, Issue. 1, p. 157.

Amann, Manuel and Kapovitch, Vitali 2012. On fibrations with formal elliptic fibers. Advances in Mathematics, Vol. 231, Issue. 3-4, p. 2048.

Calvaruso, Giovanni and Zaeim, Amirhesam 2013. Geometric Structures over Four-Dimensional Generalized Symmetric Spaces. Mediterranean Journal of Mathematics, Vol. 10, Issue. 2, p. 971.

Frey, Andrew R. and Roberts, James 2013. The dimensional reduction and Kähler metric of forms in flux and warping. Journal of High Energy Physics, Vol. 2013, Issue. 10,

Amann, Manuel 2013. Non-formal homogeneous spaces. Mathematische Zeitschrift, Vol. 274, Issue. 3-4, p. 1299.

Bocheński, Maciej and Tralle, Aleksy 2014. Generalized symplectic symmetric spaces. Geometriae Dedicata, Vol. 171, Issue. 1, p. 329.

Balashchenko, Vitaly V. 2015. Canonical distributions on Riemannian homogeneousk-symmetric spaces. Journal of Geometry and Physics, Vol. 87, Issue. , p. 30.

Goertsches, Oliver and Haghshenas Noshari, Sam 2016. Equivariant formality of isotropy actions on homogeneous spaces defined by Lie group automorphisms. Journal of Pure and Applied Algebra, Vol. 220, Issue. 5, p. 2017.

Amann, Manuel 2016. Positive curvature, symmetry, and topology. Frontiers of Mathematics in China, Vol. 11, Issue. 5, p. 1099.

Amann, Manuel and Ziller, Wolfgang 2016. Geometrically Formal Homogeneous Metrics of Positive Curvature. The Journal of Geometric Analysis, Vol. 26, Issue. 2, p. 996.

Grama, Lino Negreiros, Caio J. C. and Oliveira, Ailton R. 2017. Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers. Annali di Matematica Pura ed Applicata (1923 -), Vol. 196, Issue. 1, p. 165.

Hanke, Bernhard and Quast, Peter 2018. Γ–structures and symmetric spaces. Algebraic & Geometric Topology, Vol. 18, Issue. 2, p. 877.

Amann, Manuel 2021. Bounds on Sectional Curvature and Interactions with Topology. Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 123, Issue. 1, p. 27.

Ramani, Vimala 2023. The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds. Mathematica Slovaca, Vol. 73, Issue. 5, p. 1325.

Taimanov, Iskander 2023. On the formality problem for manifolds with special holonomy. Filomat, Vol. 37, Issue. 25, p. 8709.

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On formality of generalized symmetric spaces

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