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ON PSEUDO SEMICONFORMALLY SYMMETRIC MANIFOLDS

  • Kim, Jaeman (Department of Mathematics Education Kangwon National University)
  • Received : 2015.12.08
  • Published : 2017.01.31
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Abstract

In this paper, a type of Riemannian manifold (namely, pseudo semiconformally symmetric manifold) is introduced. Also the several geometric properties of such a manifold is investigated. Finally the existence of such a manifold is ensured by a proper example.

Keywords

References

  1. D. B. Abdussattar, On conharmonic transformations in general relativity, Bull. Calcutta Math. Soc. 88 (1996), no. 6, 465-470.
  2. A. L. Besse, Einstein Manifolds, Springer, Berlin, 1987.
  3. M. C. Chaki, On pseudo symmetric manifolds, An. Stiint Univ. Al. I. Cuza Iasi Sect. I a Mat. 33 (1987), no. 1, 53-58.
  4. M. C. Chaki, On generalized pseudo symmetric manifolds, Publ. Math. Debrecen 45 (1994), 305-312.
  5. M. C. Chaki and U. C. De, On pseudo symmetric spaces, Acta Math. Hungar. 54 (1989), 185-190. https://doi.org/10.1007/BF01952047
  6. M. C. Chaki and S. P. Mondal, On generalized pseudo symmetric manifolds, Publ. Math. Debrecen 51 (1997), 35-42.
  7. U. C. De, On weakly symmetric structures on a Riemannian manifold, Facta Univ. Ser. Mech. Automat. Control Robot. 3 (2003), no. 14, 805-819.
  8. U. C. De and A. K. Gazi, On almost pseudo symmetric manifolds, Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 51 (2008), 53-68.
  9. S. Ghosh, U. C. De, and A. Taleshian, Conharmonic curvature tensor on N(K)-contact metric manifolds, ISRN Geometry, doi:10.5402/2011/423798, 11 pages.
  10. Y. Ishii, On conharmonic transformations, Tensor (N.S.) 7 (1957), 73-80.
  11. J. Kim, A type of conformal curvature tensor, to appear in Far East J. Math. Sci.
  12. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol 1, Inter-Science, New York, 1963.
  13. C. A. Mantica and L. G. Molinari, Riemann compatible tensors, Colloq. Math. 128 (2012), no. 2, 197-210. https://doi.org/10.4064/cm128-2-5
  14. C. A. Mantica and L. G. Molinari, Weakly Z-symmetric manifolds, Acta Math. Hungarica 135 (2012), no. 1-2, 80-96. https://doi.org/10.1007/s10474-011-0166-3
  15. C. A. Mantica and Y. J. Suh, The closedness of some generalized curvature 2-forms on a Riemannian manifold I, Publ. Math. Debrecen 81 (2012), no. 3-4, 313-326. https://doi.org/10.5486/PMD.2012.5162
  16. C. A. Mantica and Y. J. Suh, Pseudo Z-symmetric Riemannian manifolds with harmonic curvature tensors, Int. J. Geom. Meth. Mod. Phys. 9 (2012), no. 1, 1250004, 21 pp. https://doi.org/10.1142/S0219887812500041
  17. C. A. Mantica and Y. J. Suh, Recurrent Z-forms on Riemannian and Kaehler manifolds, Int. J. Geom. Meth. Mod. Phys. 9 (2012), no. 7, 1250059, 26 pp. https://doi.org/10.1142/S0219887812500594
  18. F. Ozen and S. Altay, On weakly and pseudo symmetric Riemannian spaces, Indian J. Pure Appl. Math. 33 (2001), no. 10, 1477-1488.
  19. F. Ozen and A. Yavuz, Pseudo conharmonically symmetric manifolds, Eur. J. Pure Appl. Math. 7 (2014), no. 3, 246-255.
  20. W. Roter, On conformally symmetric ricci-recurrent spaces, Colloq. Math. 31 (1974), 87-96. https://doi.org/10.4064/cm-31-1-87-96
  21. W. Roter, On the existence of certain conformally recurrent metrics, Colloq. Math. 51 (1987), 315-327. https://doi.org/10.4064/cm-51-1-315-327
  22. A. A. Shaikh and S. K. Hui, On weakly conharmonically symmetric manifolds, Tensor (N.S.) 70 (2008), no. 2, 119-134.
  23. S. A. Siddiqui and Z. Ahsan, Conharmonic curvature tensor and the spacetime of general relativity, Differ. Geom. Dyn. Syst. 12 (2010), 213-220.

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