×
Funabashi, S.; Kim, H. S.; Kim, Y.-M.; Pak, J. S.

Traceless component of the conformal curvature tensor in Kähler manifold. (English) Zbl 1164.53382

Czech. Math. J. 56, No. 3, 857-874 (2006).
Summary: We investigate the traceless component of the conformal curvature tensor in Kähler manifolds of dimension \(\geq 4\), 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 concerning 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 traceless component.

Cited in 1 Document

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds

Keywords:

Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum
PDF BibTeX XML Cite
\textit{S. Funabashi} et al., Czech. Math. J. 56, No. 3, 857--874 (2006; Zbl 1164.53382)
Full Text: DOI EuDML Link
  • logo of hbz
  • logo of WorldCat

References:

[1] M. Berger, P. Gauduchon et E. Mazet: Le Spectre d’une Variété Riemannienne. Lecture Notes in Mathematics 194, Springer-Verlag, 1971. · Zbl 0223.53034
[2] H. Kitahara, K. Matsuo and J. S. Pak: A conformal curvature tensor field on hermitian manifolds; Appendium. J. Korean Math. Soc.; Bull. Korean Math. Soc. 27 (1990), 7–17; 27–30. · Zbl 0711.53020
[3] D. Krupka: The trace decomposition problem. Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry 36 (1995), 303–315. · Zbl 0839.15024
[4] 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), 309–319. · Zbl 0845.53046
[5] V. K. Patodi: Curvature and the fundamental solution of the heat operator. J. Indian Math. Soc. 34 (1970), 269–285. · Zbl 0237.53039
[6] S. Tachibana: Riemannian Geometry. Asakura Shoten, Tokyo, 1967. (In Japanese.)
[7] S. Tanno: Eigenvalues of the Laplacian of Riemannian manifolds. Tôhoku Math. J. 25 (1973), 391–403. · Zbl 0266.53033
[8] Gr. Tsagas: On the spectrum of the Laplace operator for the exterior 2-forms. Tensor N. S. 33 (1979), 94–96. · Zbl 0408.53026
[9] S. Yamaguchi and G. Chuman: Eigenvalues of the Laplacian of Sasakian manifolds. TRU Math. 15 (1979), 31–41. · Zbl 0432.53029
[10] K. Yano: Differential Geometry on complex and almost complex spaces. Pergamon Press, New York, 1965. · Zbl 0127.12405
[11] K. Yano and S. Ishihara: Kaehlerian manifolds with constant scalar curvature whose Bochner curvature tensor vanishes. Hokkaido Math. J. 3 (1974), 297–304. · Zbl 0291.53032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.