Traceless component of the conformal curvature tensor in Kähler manifold

Shoichi Funabashi; Hyang Sook Kim; Y.-M. Kim; Jin Suk Pak

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 857-874
  • ISSN: 0011-4642

Abstract

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We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension ≥ 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 (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on p ( 0 ≤ p ≤ 2 ) -forms on the manifold by using the traceless component.

How to cite

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Funabashi, Shoichi, et al. "Traceless component of the conformal curvature tensor in Kähler manifold." Czechoslovak Mathematical Journal 56.3 (2006): 857-874. <http://eudml.org/doc/31072>.

@article{Funabashi2006,
abstract = {We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension $\ge 4$, 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 (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on $p$$(0\le p\le 2)$-forms on the manifold by using the traceless component.},
author = {Funabashi, Shoichi, Kim, Hyang Sook, Kim, Y.-M., Pak, Jin Suk},
journal = {Czechoslovak Mathematical Journal},
keywords = {Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum; Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum},
language = {eng},
number = {3},
pages = {857-874},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Traceless component of the conformal curvature tensor in Kähler manifold},
url = {http://eudml.org/doc/31072},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Funabashi, Shoichi
AU - Kim, Hyang Sook
AU - Kim, Y.-M.
AU - Pak, Jin Suk
TI - Traceless component of the conformal curvature tensor in Kähler manifold
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 857
EP - 874
AB - We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension $\ge 4$, 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 (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on $p$$(0\le p\le 2)$-forms on the manifold by using the traceless component.
LA - eng
KW - Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum; Kähler manifold; conformal tensor field; trace decomposition; concircular transformation; spectrum
UR - http://eudml.org/doc/31072
ER -

References

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  7. 10.2748/tmj/1178241341, Tôhoku Math. J. 25 (1973), 391–403. (1973) Zbl0266.53033MR0334086DOI10.2748/tmj/1178241341
  8. On the spectrum of the Laplace operator for the exterior 2-forms, Tensor N. S. 33 (1979), 94–96. (1979) Zbl0408.53026MR0577217
  9. Eigenvalues of the Laplacian of Sasakian manifolds, TRU Math. 15 (1979), 31–41. (1979) MR0564366
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  11. 10.14492/hokmj/1381758810, Hokkaido Math. J. 3 (1974), 297–304. (1974) MR0362170DOI10.14492/hokmj/1381758810

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