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Invariant nearly-Kähler structures

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Abstract

This paper considers invariant almost Hermitian structures on a flag manifold G / P = U / K where G is a complex semi-simple Lie group, P is a parabolic subgroup of G, U is a compact real form of G and K = U ∩ P is the centralizer of a torus. The main result shows that there are nearly-Kähler structures in G / P which are not Kähler if and only if G / P has height two. This proves for the flag manifolds a conjecture by Wolf and Gray.

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Authors and Affiliations

  1. Departamento de Matemática Imecc, Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-970, Campinas, SP, Brasil

    Luiz A. B. San Martin

  2. Instituto de Matemática, Universidade Federal da Bahia – UFBA, Av. Ademar de Barros s/n, 40.170-110, Salvador, BA, Brasil

    Rita de Cássia de J. Silva

Authors
  1. Luiz A. B. San Martin
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  2. Rita de Cássia de J. Silva
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Correspondence to Luiz A. B. San Martin.

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Martin, L.A.B.S., Silva, R.d.C.d.J. Invariant nearly-Kähler structures. Geom Dedicata 121, 143–154 (2006). https://doi.org/10.1007/s10711-006-9095-7

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  • DOI: https://doi.org/10.1007/s10711-006-9095-7

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