Kyungpook Mathematical Journal

  • 제51권1호
  • /
  • Pages.109-124
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  • 2011
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On Quasi-Conformally Recurrent Manifolds with Harmonic Quasi-Conformal Curvature Tensor

  • 투고 : 2010.08.04
  • 심사 : 2011.02.09
  • 발행 : 2011.03.31
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초록

The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

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참고문헌

  1. T. Adati and T. Miyazawa, On Riemannian space with recurrent conformal curvature, Tensor (N.S.), 18(1967), 348-354.
  2. K. Amur and Y. B. Maralabhavi, On quasi-conformally at spaces, Tensor (N.S.), 31(1977), 194-198.
  3. M. C. Chaki and B. Gupta, On conformally symmetric spaces, Indian J. Math., 5(1963), 113-122.
  4. A. Derdzinski and W. Roter, Some theorems on conformally symmetric manifolds, Tensor (N.S.), 32(1978), 11-23.
  5. U. C. De and A. A. Shaikh, On quasi-conformally recurrent manifolds, Istanbul Univ. Fen Fak. Mat. Dergisi, 55-56(1996-1997), 213-220.
  6. L. P. Eisenhart, Riemannian geometry, Princeton University Press, Princeton, 1934.
  7. D. Ferus, A remark on codazzi tensors on constant curvature space. In D. Ferus, W. Kuhnel, and B. Wegur, editors, Global differential geometry and global analysis, volume 838 of Lecture notes in Mathematics. Springer, 1981.
  8. S. Goldberg and M. Okumura, Conformally at manifolds and a pinching problem on the Ricci tensor, Proc. Amer. Math. Soc., 58(1976), 234-236. https://doi.org/10.1090/S0002-9939-1976-0410601-9
  9. D. Lovelock and H. Rund, Tensors, differential forms and variational principles, reprint Dover Ed., 1988.
  10. T. Miyazawa, Some theorems on conformally symmetric spaces, Tensor (N.S.), 32(1978), 24-26.
  11. W. Roter, On a generalization of conformally symmetric metrics, Tensor (N.S.), 46(1987), 278-286.
  12. J. A. Schouten, Ricci-Calculus. An introduction to tensor analysis and its geometrical applications. Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstel-lungen mit besonderer Berucksichtigung der Anwendungsgebiete, Bd X. Springer-Verlag, Berlin, 1954, 2nd. ed.
  13. A. A. Shaikh and T. Q. Binh, On some class of Riemannian manifolds, Bull. Tran- silvania Univ., Brasov, 15(50), III, (2008), 351-362.
  14. Y. J. Suh, J. O. Baek and J. H. Kwon, Conformally recurrent Riemannian manifolds with harmonic conformal curvature tensor, Kyungpook Math. J., 44(2004), 47-61.
  15. A. G. Walker, On Ruse's spaces of recurrent curvature, Proc. London Math. Soc., 52(1950), 36-64. https://doi.org/10.1112/plms/s2-52.1.36
  16. K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2(1968), 161-184. https://doi.org/10.4310/jdg/1214428253