$F$-traceless component of the conformal curvature tensor on Kahler manifold
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 795-806
Published online December 1, 2007
Shoichi Funabashi, Hang Sook Kim, Young-Mi Kim, and Jin Suk Pak
Nippon Institute of Technology, Inje University, Inje University, Kyungpook National University
Abstract : We investigate $F$-traceless component of the conformal curvature tensor defined by (3.6) in K\"ahler manifolds of dimension $\geq 4$, and show that the $F$-traceless component is invariant under concircular change. In particular, we determine K\"ahler manifolds with parallel $F$-traceless component and improve some theorems, provided in the previous paper ([2]), which are concerned with the traceless component of 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 $F$-traceless component.
Keywords : Kahler manifold, conformal curvature tensor, traceless decomposition, $F$-traceless decomposition, constant holomorphic sectional curvature, spectrum
MSC numbers : 53C
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