Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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QUASI-CONFORMAL CURVATURE TENSOR ON N (k)-QUASI EINSTEIN MANIFOLDS

  • Received : 2021.09.30
  • Accepted : 2021.12.09
  • Published : 2021.12.30
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Abstract

This paper deals with the study of N (k)-quasi Einstein manifolds that satisfies the certain curvature conditions 𝒞*·𝒞* = 0, 𝓢·𝒞* = 0 and ${\mathcal{R}}{\cdot}{\mathcal{C}}_*=f{\tilde{Q}}(g,\;{\mathcal{C}}_*)$, where 𝒞*, 𝓢 and 𝓡 denotes the quasi-conformal curvature tensor, Ricci tensor and the curvature tensor respectively. Finally, we construct an example of N (k)-quasi Einstein manifold.

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References

  1. K. Amur and Y. B. Maralabhavi, On quasi-conformally at spaces, Tensor (N.S.), 31 (1977), 194-198.
  2. C. L. Bejan, Characterization of quasi-Einstein manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(NS), 53 (2007), 67-72.
  3. M. C. Chaki and R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen, 57(2000), 297-306. https://doi.org/10.5486/PMD.2000.2169
  4. B. Y. Chen and K. Yano, Special conformally at spaces and canal hypersurfaces, Tohoku Mathematical Journal, 25 (1973), 177-184. https://doi.org/10.2748/tmj/1178241376
  5. M. Crasmareanu, Parallel tensors and Ricci solitons in N(k)-quasi Einstein manifolds, Indian Journal of Pure and Applied Mathematics, 43 (2012), 359-369. https://doi.org/10.1007/s13226-012-0022-3
  6. U. C. De and B. K. De, On quasi-Einstein manifolds, Communications of the Korean Mathematical Society, 23 (2008), 413-420. https://doi.org/10.4134/CKMS.2008.23.3.413
  7. A. De, U. C. De and A. K. Gazi, On a class of N(k)-quasi Einstein manifolds, Commun. Korean Math. Soc., 26 (2011), 623-634. https://doi.org/10.4134/CKMS.2011.26.4.623
  8. U. C. De and G. C. Ghosh, On quasi Einstein manifolds, Periodica Mathematica Hungarica, 48 (2004), 223-231. https://doi.org/10.1023/B:MAHU.0000038977.94711.ab
  9. P. Debnath and A. Konar, On quasi-Einstein manifolds and quasi-Einstein spacetimes, Differ. Geom. Dyn. Syst., 12 (2010), 73-82.
  10. R. Deszcz, On pseudosymmetric space, Bull. Soc. Math. Belg., Ser. A, 44 (1992), 1-34.
  11. S. Guha, On quasi Einstein and generalized quasi Einstein manifolds, Facta universitatis-series: Mechanics, Automatic Control and Robotics, 3 (2003), 821-842.
  12. A. A. Hosseinzadeh and A. Taleshian, On conformal and quasi-conformal curvature tensors of an N(k)-quasi Einstein manifolds, Communications of the Korean Mathematical Society, 27 (2012), 317-326. https://doi.org/10.4134/CKMS.2012.27.2.317
  13. S. Mallick and U. C. De, Z Tensor on N(k)-Quasi-Einstein Manifolds, Kyungpook Mathematical Journal, 56 (2016), 979-991. https://doi.org/10.5666/KMJ.2016.56.3.979
  14. C. Ozgur and S. Sular, On N(k)-quasi Einstein manifolds satisfying certain conditions, Balkan J. Geom. Appl., 13 (2008), 74-79.
  15. C. Ozgur and M. M. Tripathi, On the concircular curvature tensor of an N(k)-quasi Einstein manifold, Math. Pannon, 18 (2007), 95-100.
  16. A. Taleshian and A. A. Hosseinzadeh, Investigation of Some Conditions on N(k)-quasi Einstein Manifolds, Bulletin of the Malaysian Mathematical Sciences Society, 34 (2011), 455-464.
  17. S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Mathematical Journal, Second Series, 40 (1988), 441-448.
  18. M. M. Tripathi and J. S. Kim, On N(k)-quasi Einstein manifolds, Communications of the Korean Mathematical Society, 22 (2007), 411-417. https://doi.org/10.4134/CKMS.2007.22.3.411
  19. K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, Journal of Differential Geometry, 2 (1968), 161-184.
  20. A. Yildiz, U. C. De and A. Cetinkaya, On some classes of N(k)-quasi Einstein manifolds, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 83 (2013), 239-245. https://doi.org/10.1007/s40010-013-0071-y