Invariant almost Hermitian structures on flag manifolds.

DOI10.1016/S0001-8708(02)00073-7zbMath1044.53053OpenAlexW2026785539MaRDI QIDQ1408804

Luiz A. B. San Martin, Caio J. C. Negreiros

Publication date: 25 September 2003

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0001-8708(02)00073-7

zbMATH Keywords

flag manifoldharmonic mapsemi-simple Lie groupaffine Weyl groupHermitian structureAbelian ideal of Borel subalgebra

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Differential geometry of homogeneous manifolds (53C30) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Harmonic maps, etc. (58E20)

Related Items (23)

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$ ⋮ Killing-Yano 2-forms on homogeneous spaces ⋮ Invariant nearly-Kähler structures ⋮ Controllability of control systems on complex simple Lie groups and the topology of flag manifolds ⋮ Invariant generalized complex structures on flag manifolds ⋮ Invariant generalized complex geometry on maximal flag manifolds and their moduli ⋮ Second homotopy group and invariant geometry of flag manifolds ⋮ Scalar curvatures of invariant almost Hermitian structures on flag manifolds with two and three isotropy summands ⋮ Geometric realizability of covariant derivative Kähler tensors for almost pseudo-Hermitian and almost para-Hermitian manifolds ⋮ Adjoint Orbits of Semi-Simple Lie Groups and Lagrangian Submanifolds ⋮ Variational aspects of homogeneous geodesics on generalized flag manifolds and applications ⋮ Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers ⋮ Invariant almost complex structures on real flag manifolds ⋮ Equigeodesics on generalized flag manifolds with two isotropy summands ⋮ Variational results on flag manifolds: harmonic maps, geodesics and Einstein metrics ⋮ Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds ⋮ On the stability of invariant almost complex structures on flag manifolds ⋮ Invariant \({\mathcal{G}}_1\) structures on flag manifolds ⋮ Equi-harmonic maps and Plücker formulae for horizontal-holomorphic curves on flag manifolds ⋮ Scalar curvatures of invariant almost Hermitian structures on generalized flag manifolds ⋮ Invariant generalized complex structures on partial flag manifolds ⋮ \(f\)-structures on the classical flag manifold which admit \((1,2)\)-symplectic metrics ⋮ The isotropy representation of a real flag manifold: split real forms

Cites Work

• Tournaments, flags, and harmonic maps
• The sixteen classes of almost Hermitian manifolds and their linear invariants
• \((1,2)\)-symplectic structures on flag manifolds
• Families of \((1,2)\)-symplectic metrics on full flag manifolds
• A rank-three condition for invariant (1,2)-symplectic almost Hermitian structures on flag manifolds
• Minimal varieties and almost Hermitian submanifolds
• Homogeneous spaces defined by Lie group automorphisms. I
• Homogeneous spaces defined by Lie group automorphisms. II
• (1, 2)-SYMPLECTIC METRICS, FLAG MANIFOLDS AND TOURNAMENTS
• Alcoves Corresponding to an Affine Weyl Group
• Kählerian Coset Spaces of Semisimple Lie Groups
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