Advertisement

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

  • Nir Cohen
  • Caio J.C. Negreiros
  • Luiz A.B. San Martin
Article

Abstract.

This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not Bl , l ≥ 3, G2 or F4. For Bl and F4 a close condition turns out to be sufficient.

Keywords: Semi-simple Lie groups, flag manifolds, affine Weyl groups, Hermitian geometry. 
Mathematical subject classification: 22F30, 20F55, 53C55. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Sociedade Brasileira de Matemática 2002

Authors and Affiliations

  • Nir Cohen
    • 1
  • Caio J.C. Negreiros
    • 2
  • Luiz A.B. San Martin
    • 3
  1. 1.Department of Applied MathematicsBrazil
  2. 2.Department of MathematicsBrazil
  3. 3.Department of Mathematics, Imecc Universidade Estadual de Campinas, Cx. Postal 6065 13.083-970 Campinas, - SP. BRASIL E-mail: nir@ime.unicamp.br / caione@ime.unicamp.br / smartin@ime.unicamp.brBrazil

Personalised recommendations