Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON A CLASS OF N(κ)-QUASI EINSTEIN MANIFOLDS

  • De, Avik (Department of Pure Mathematics University of Calcutta) ;
  • De, Uday Chand (Department of Pure Mathematics University of Calcutta) ;
  • Gazi, Abul Kalam (Moynagodi E.B.A.U. High Madrasah)
  • Received : 2010.04.12
  • Published : 2011.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

The object of the present paper is to study N(${\kappa}$)-quasi Einstein manifolds. Existence of N(${\kappa}$)-quasi Einstein manifolds are proved. Physical example of N(${\kappa}$)-quasi Einstein manifold is also given. Finally, Weyl-semisymmetric N(${\kappa}$)-quasi Einstein manifolds have been considered.

Keywords

References

  1. T. Adati and G. Chuman, Special para-Sasakian manifolds D-conformal to a manifold of constant curvature, TRU Math. 19 (1983), no. 2, 179-193.
  2. T. Adati and G. Chuman, Special para-Sasakian manifolds and concircular transformations, TRU Math. 20 (1984), no. 1, 111-123.
  3. T. Adati and T. Miyazawa, On paracontact Riemannian manifolds, TRU Math. 13 (1977), no. 2, 27-39.
  4. A. L. Besse, Einstein Manifolds, Ergeb. Math. Grenzgeb., 3. Folge, Bd. 10, Springer- Verlag, Berlin, Heidelberg, New York, 1987.
  5. M. C. Chaki, On generalized quasi-Einstein manifolds, Publ. Math. Debrecen 58 (2001), no. 4, 683-691.
  6. M. C. Chaki, On pseudo Ricci-symmetric manifolds, Bulg. J. Physics 15 (1988), 526-531.
  7. M. C. Chaki and B. Gupta, On conformally symmetric spaces, Indian J. Math. 5 (1963), 113-122.
  8. M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen, 57 (2000), no. 3-4, 297-306.
  9. G. Chuman, D-conformal changes in para-Sasakian manifolds, Tensor (N.S.) 39 (1982), 117-123.
  10. U. C. De and A. K. Gazi, On pseudo Ricci symmetric manifolds, to appear in Anl. Stiintifice Ale Universitataii "Al. I. CUZA" Iasi. Matematica.
  11. U. C. De and G. C. Ghosh, On quasi Einstein and special quasi Einstein manifolds, Proc. of the Int. Conf. of Mathematics and its applications, Kuwait University, April 5-7, 2004, 178-191.
  12. U. C. De and G. C. Ghosh, On quasi-Einstein manifolds, Period. Math. Hungar. 48 (2004), no. 1-2, 223-231. https://doi.org/10.1023/B:MAHU.0000038977.94711.ab
  13. U. C. De and G. C. Ghosh, On conformally flat special quasi-Einstein manifolds, Publ. Math. Debrecen 66 (2005), no. 1-2, 129-136.
  14. R. Deszcz, M. Hotlos, and Z. Senturk, On curvature properties of quasi-Einstein hyper- surfaces in semi-Euclidean spaces, Soochow J. Math. 27 (2001), no. 4, 375-389.
  15. A. Einstein, Grundzuge der relativitats theory, Berlin, Springer, 2002.
  16. M. S. El Naschie, Is Einstein's general eld equation more fundamental than quantum field theory and particle physics?, Chaos, Solutions and Fractals 30 (2006), no. 3, 525-531. https://doi.org/10.1016/j.chaos.2005.04.123
  17. M. S. El Naschie, Godel universe, dualities and high energy particle in E-infinity, Chaos, Solutions and Fractals 25 (2005), no. 3, 759-764. https://doi.org/10.1016/j.chaos.2004.12.010
  18. S. R. Guha, On quasi-Einstein and generalized quasi-Einstein manifolds, Facta Univ. Ser. Mech. Automat. Control Robot. 3 (2003), no. 14, 821-842.
  19. C. Ozgur, N(k)-quasi Einstein manifolds satisfying certain conditions, Chaos Solitons Fractals 38 (2008), no. 5, 1373-1377. https://doi.org/10.1016/j.chaos.2008.03.016
  20. C. Ozgur and M. M. Tripathi, On the concircular curvature tensor of an N(k)-quasi Einstein manifold, Math. Pannon. 18 (2007), no. 1, 95-100.
  21. F. Ozen and S. Altay, On weakly and pseudo-symmetric Riemannian spaces, Indian J. Pure appl. Math. 33 (2002), 1477-1488.
  22. S. Ray-Guha, On perfect uid pseudo Ricci symmetric spacetime, Tensor, N. S. 67 (2006), 101-107.
  23. R. N. Sen and M. C. Chaki, On curvature restriction of a certain kind of conformally at Riemannian spaces of class-one, Proc. Nat. Inst. Sci. India Part A 33 (1967), 100-102.
  24. R. Sharma, Proper conformal symmetries of conformal symmetric space-times, J. Math. Phys. 29 (1988), no. 11, 2421-2422. https://doi.org/10.1063/1.528127
  25. H. Stephant, Some new algebraically special radiation field solutions connected with Hauser's type N vacuum solution, Abstracts of GR9, Jena. 1980.
  26. Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X,Y)${\cdot}$R = 0. I. The local version, J. Differential Geom. 17 (1982), no. 4, 531-582.
  27. Z. I. Szabo, Classification and construction of complete hypersurfaces satisfying R(X,Y)${\cdot}$R = 0, Acta Sci. Math. (Szeged) 47 (1984), no. 3-4, 321-348.
  28. Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X,Y)${\cdot}$R = 0. II. Global version, Geom. Dedicata 19 (1985), no. 1, 65-108.
  29. L. Tamassy and T. Q. Binh, On weakly symmetries of Einstein and Sasakian manifolds, Tensor. N. S. 53 (1993), 140-148.
  30. S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tohoku Math. J. (2) 40 (1988), no. 3, 441-448. https://doi.org/10.2748/tmj/1178227985
  31. M. M. Tripathi and J. S. Kim, On N(k)-quasi Einstein manifolds, Commun. Korean Math. Soc. 22 (2007), no. 3, 411-417. https://doi.org/10.4134/CKMS.2007.22.3.411

Cited by

  1. Quantum Disentanglement as the Physics behind Dark Energy vol.07, pp.01, 2017, https://doi.org/10.4236/ojm.2017.71001
  2. The Speed of the Passing of Time as Yet Another Facet of Cosmic Dark Energy vol.07, pp.15, 2016, https://doi.org/10.4236/jmp.2016.715184
  3. On Some Classes of N(k)-Quasi Einstein Manifolds vol.83, pp.3, 2013, https://doi.org/10.1007/s40010-013-0071-y
  4. Cantorian-Fractal Kinetic Energy and Potential Energy as the Ordinary and Dark Energy Density of the Cosmos Respectively vol.08, pp.12, 2016, https://doi.org/10.4236/ns.2016.812052
  5. Completing Einstein’s Spacetime vol.07, pp.15, 2016, https://doi.org/10.4236/jmp.2016.715175
  6. 𝒵 Tensor on N(k)-Quasi-Einstein Manifolds vol.56, pp.3, 2016, https://doi.org/10.5666/KMJ.2016.56.3.979
  7. Certain results on N(k)-quasi Einstein manifolds pp.2190-7668, 2019, https://doi.org/10.1007/s13370-018-0631-z