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arXiv · 1802.07970

The exterior derivative of the Lee form of almost Hermitian manifolds

Francisco Martín Cabrera
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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 $\mathbb{R}ω$-component of $dθ$ is always zero. expressions for the other components, in $[λ_0^{1,1}]$ 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.

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Francisco Martín Cabrera. 2019-11-28. The exterior derivative of the Lee form of almost Hermitian manifolds. https://arxiv.org/abs/1802.07970

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