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$F$-traceless component of the conformal curvature tensor on K\"ahler manifold

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Abstract

We investigate F-traceless component of the conformal cur-vature tensor dened by (3.6) in K¨ahler manifolds of dimension 4,and show that the F-traceless component is invariant under concircu-lar change. In particular, we determine K¨ahler manifolds with parallelF-traceless component and improve some theorems, provided in the pre-vious paper ([2]), which are concerned with the traceless component of theconformal curvature tensor and the spectrum of the Laplacian acting onp (0 p 2)-forms on the manifold by using the F-traceless component.

참고문헌 (13)

  1. "Lec-ture Notes in Mathematics 194" (1971), Springer-Verlag
  2. "Traceless component of the confor-mal curvature tensor in K¨ahler manifold", 56, pp.857~874 (2006)
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  4. "Appendium; A conformal curvature tensor eld on hermitian manifolds" (1990)
  5. "The trace decomposition problem", 36(2), pp.303~315 (1995)
  6. "The decomposition of tensor spaces with almost complex structure", 2(72), pp.145~150 (2004)
  7. "On general trace decomposition problem, Proc. Conf., Aug. 28-Sept. 1", pp.45~50 (1995)
  8. "Conformal curvature tensor eld and spectrumof the Laplacian in Kaehlerian manifolds", 32(2), pp.309~319 (1995)
  9. "Curvature and the fundamental solution of the heat operator", pp.3~4 (1970)
  10. "Eigenvalues of the Laplacian of Riemannian manifolds", tan (1973)
  11. "On the spectrum of the Laplace operator for the exterior2-forms" (1979)
  12. "Eigenvalues of the Laplacian of Sasakian manifolds" (1979)
  13. "Dierential geometry on complex and almost complex spaces InternationalSeries of Monographs in Pure and Applied Mathematics", ya, pp.806~ (1965), A Pergamon PressBook The Macmillan Co

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