# F-TRACELESS COMPONENT OF THE CONFORMAL CURVATURE TENSOR ON KÄHLER MANIFOLD

• Funabashi, Shoichi (DEPARTMENT OF MATHEMATICS NIPOPON INSTITUTE OF TECHNOLOGY) ;
• Kim, Hang-Sook (DEPARTMENT OF COMPUTATIONAL MATHEMATICS SCHOOL OF COMPUTER AIDED SCIENCE AND INSTITUTE OF MATHEMATICAL SCIENCES COLLEGE OF NATURAL SCIENCE, INJE UNIVERSITY) ;
• Kim, Young-Mi (DEPARTMENT OF COMPUTATIONAL MATHEMATICS SCHOOL OF COMPUTER AIDED SCIENCE AND INSTITUTE OF MATHEMATICAL SCIENCES COLLEGE OF NATURAL SCIENCE, INJE UNIVERSITY) ;
• Pak, Jin-Suk (DEPARTMENT OF MATHEMATICS EDUCATION KYUNGPOOK NATIONAL UNIVERSITY)
• Published : 2007.11.30
• 57 2

#### Abstract

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ 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

$K\ddot{a}hler$ manifold;conformal curvature tensor;traceless decomposition;F-traceless decomposition;constant holomorphic sectional curvature;spectrum

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