JOURNAL BROWSE
Search
Advanced SearchSearch Tips
F-TRACELESS COMPONENT OF THE CONFORMAL CURVATURE TENSOR ON KÄHLER MANIFOLD
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
F-TRACELESS COMPONENT OF THE CONFORMAL CURVATURE TENSOR ON KÄHLER MANIFOLD
Funabashi, Shoichi; Kim, Hang-Sook; Kim, Young-Mi; Pak, Jin-Suk;
  PDF(new window)
 Abstract
We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in manifolds of dimension , and show that the F-traceless component is invariant under concircular change. In particular, we determine 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 -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
manifold;conformal curvature tensor;traceless decomposition;F-traceless decomposition;constant holomorphic sectional curvature;spectrum;
 Language
English
 Cited by
 References
1.
M. Berger, P. Gauduchon, and E. Mazet, Le Spectre d'une Variete riemannienne, Lecture Notes in Mathematics 194, Springer-Verlag, 1971

2.
S. Funabashi, H. S. Kim, Y.-M. Kim, and J. S. Pak, Traceless component of the confor- mal curvature tensor in Kahler manifold, Czech. Math. J. 56 (2006), 857-874 crossref(new window)

3.
H. Kitahara, K. Matsuo, and J. S. Pak, A conformal curvature tensor field on hermitian manifolds, J. Korean Math. Soc. 27 (1990), 7-17

4.
H. Kitahara, K. Matsuo, and J. S. Pak, Appendium; A conformal curvature tensor field on hermitian manifolds, Bull. Korean Math. Soc. 27 (1990), 27-30

5.
D. Krupka, The trace decomposition problem, Beitrage Algebra Geom. 36 (1995), no. 2, 303-315

6.
L. Lakoma and M. Jukl, The decomposition of tensor spaces with almost complex struc- ture, Rend. Circ. Mat. Palermo (2) Suppl. No. 72 (2004), 145-150

7.
L. Mikes, On general trace decomposition problem, Proc. Conf., Aug. 28-Sept. 1, Brno, Czech Rep. (1995), 45-50

8.
J. S. Pak, K.-H. Cho, and J.-H. Kwon, Conformal curvature tensor field and spectrum of the Laplacian in Kaehlerian manifolds, Bull. Korean Math. Soc. 32 (1995), no. 2, 309-319

9.
V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), no. 3-4, 269-285

10.
S. Tachibana, Riemannian geometry, Asakura Shoten, Tokyo, 1967

11.
S. Tanno, Eigenvalues of the Laplacian of Riemannian manifolds, Tohoku Math. J. (2) 25 (1973), 391-403 crossref(new window)

12.
Gr. Tsagas, On the spectrum of the Laplace operator for the exterior 2-forms, Tensor(N.S.) 33 (1979), no. 1, 94-96

13.
S. Yamaguchi and G. Chuman, Eigenvalues of the Laplacian of Sasakian manifolds, TRU Math. 15 (1979), no. 2, 31-41

14.
K. Yano, Differential geometry on complex and almost complex spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 49, A Pergamon Press Book, The Macmillan Co., New York, 1965