Pluriclosed metrics on compact semisimple Lie groups

2025/06/26 by Jorge Lauret, Lauret, Jorge, Facundo Montedoro +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2506.21725

openalex publication_date 2025/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compact semisimple Lie group G and a maximal torus T of G, we give an explicit description of all left and Ad(T)-invariant pluriclosed Hermitian structures on G in terms of the corresponding root system. They depend on 2d+1 parameters in the irreducible case, where dim(T)=2d. As applications, we obtain that the only left and Ad(T)-invariant pluriclosed metrics which are also CYT are bi-invariant metrics (i.e., Bismut flat) and study the pluriclosed flow as a neat ODE system.

Citations

• Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow
• Harmonic 3-forms on compact homogeneous spaces
• On the pluriclosed flow on Oeljeklaus-Toma manifolds
• SKT structures on nilmanifolds
• Hermitian structures on a class of almost nilpotent solvmanifolds
• Real semisimple Lie groups and balanced metrics
• Non-Kähler Calabi-Yau geometry and pluriclosed flow
• Two-step solvable SKT shears
• Homogeneous Hermitian manifolds and special metrics
• On the Chern-Ricci flow and its solitons for Lie groups
• A note about invariant SKT structures and generalized Kahler structures\n on flag manifolds
• Geometry of compact complex homogeneous spaces with vanishing first Chern class
• Hermitian Curvature Flow

Related

• Pluriclosed and Strominger Kähler-like metrics compatible with abelian complex structures
• Bismut Hermitian Einstein metrics and the stability of the pluriclosed flow
• Real semisimple Lie groups and balanced metrics
• Streets-Tian Conjecture on several special types of Hermitian manifolds
• Semi-Riemannian metrics on compact simple Lie Groups