Geodesic
Traceless component of the conformal curvature tensor in Kähler manifold
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 857-874
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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.
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.
Classification : 53C55, 58J50
Keywords: Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum 
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     author = {Funabashi, Shoichi and Kim, Hyang Sook and Kim, Young-Mi and Pak, Jin Suk},
     title = {Traceless component of the conformal curvature tensor in {K\"ahler} manifold},
     journal = {Czechoslovak Mathematical Journal},
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Funabashi, Shoichi; Kim, Hyang Sook; Kim, Young-Mi; Pak, Jin Suk. Traceless component of the conformal curvature tensor in Kähler manifold. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 857-874. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a4/

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