The exterior derivative of the Lee form of almost Hermitian manifolds

Abstract

The exterior derivative $d\theta$ of the Lee form $\theta$ of almost Hermitian manifolds is studied. If $\omega$ is the Kähler two-form, it is proved that the $\mathbb{R}\omega$-component of $d\theta$ is always zero. expressions for the other components, in $[{\lambda }_0^{1,1}]$ and in $[[{\lambda }^{2,0}]]$, of $d\theta$ 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.

arXiv comment18 pages, to appear in Journal of Geometry and Physics

References in corpus (2)

• Almost Hermitian Geometry on Six Dimensional Nilmanifolds
• Special almost Hermitian geometry

Cited by in corpus (1)

• Harmonic almost contact metric manifolds revisited