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Keywords:
Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum
Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum
Summary:
We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension $\ge 4$, 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 (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on $p$ $(0\le p\le 2)$-forms on the manifold by using the traceless component.
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