Traceless component of the conformal curvature tensor in Kähler manifold. (English) Zbl 1164.53382

Summary: We investigate the traceless component of the conformal curvature tensor in Kähler manifolds of dimension \(\geq 4\), and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems concerning the conformal curvature tensor and the spectrum of the Laplacian acting on \(p\) \((0\leq p\leq 2)\)-forms on the manifold by using the traceless component.


53C55 Global differential geometry of Hermitian and Kählerian manifolds
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