The exterior derivative of the Lee form of almost Hermitian manifolds

The exterior derivative of the Lee form of almost Hermitian manifolds

The exterior derivative dθ 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 [λ01,1] and in [[λ2,0]], of dθ are also obtained. They are given in terms of the intri...

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Veröffentlicht in:Journal of geometry and physics 2020-02, Vol.148, p.103563, Article 103563
1. Verfasser: Martín Cabrera, Francisco
Format: Artikel
Sprache:eng
Schlagworte:
[formula omitted]-structure
Almost Hermitian
Intrinsic torsion
Lee-form
Minimal connection
Ricci curvature
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Zusammenfassung:The exterior derivative dθ 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 [λ01,1] and in [[λ2,0]], 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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2019.103563