The exterior derivative of the Lee form of almost Hermitian manifolds

2018/02/22 by Francisco Martı́n Cabrera, Francisco Martín Cabrera, Cabrera, Francisco Martín
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1802.07970

18 pages, to appear in Journal of Geometry and Physics

openalex publication_date 2018/02/22 · arxiv created 2019/11/28 · arxiv updated 2019/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The exterior derivative d θ of the Lee form θ of almost Hermitian manifolds is studied. If ω is the Kähler two-form, it is proved that the ℝω-component of dθ is always zero. expressions for the other components, in [λ₀^1,1] and in [[ λ^2,0 ]], of dθ are also obtained. They are given in terms of the intrinsic torsion. Likewise, it is described some interrelations between the Lee form and U(n)-components of the Riemannian curvature tensor.

Citations

• Complex structures on nilpotent Lie algebras
• Almost Hermitian Geometry on Six Dimensional Nilmanifolds

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• Scalar curvatures in almost Hermitian geometry and some applications
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