Almost Kaehler geometry of adjoint orbits of semisimple Lie groups

2018/11/16 by Alberto Della Vedova, Alice Gatti, Della Vedova, Alberto +1
Mathematics · #22E46 (Secondary) #53C25 (Primary) #53C30 #53D05 #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1811.06958

openalex publication_date 2018/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the Chern-Ricci form, the Hermitian scalar curvature and the Nijenhuis tensor in terms of root data. We also discuss when the Chern-Ricci form is a multiple of the symplectic form, and when compact quotients of these orbits are of Kaehler type.

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