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

Title & Authors
F-TRACELESS COMPONENT OF THE CONFORMAL CURVATURE TENSOR ON KÄHLER MANIFOLD
Funabashi, Shoichi; Kim, Hang-Sook; Kim, Young-Mi; Pak, Jin-Suk;

Abstract
We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $\small{K\ddot{a}hler}$ manifolds of dimension $\small{{\geq}4}$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $\small{K\ddot{a}hler}$ 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 $\small{p(0{\leq}p{\leq}2)}$-forms on the manifold by using the F-traceless component.ﾖ⨀✌넀؀㔷〮㔻ᜀ䱩晥⁳捩敮捥猠☠扩潬潧礀
Keywords
$\small{K\ddot{a}hler}$ manifold;conformal curvature tensor;traceless decomposition;F-traceless decomposition;constant holomorphic sectional curvature;spectrum;
Language
English
Cited by
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