About this Journal Submit a Manuscript Table of Contents
ISRN Geometry
Volume 2012 (2012), Article ID 217132, 10 pages
http://dx.doi.org/10.5402/2012/217132
Research Article

Some Results on Super Quasi-Einstein Manifolds

1Nikhil Banga Sikshan Mahavidyalaya, Bishnupur, 722122 West Bengal, Bankura, India
2Institute of Mathematics College of Science, University of the Philippines Diliman, Quezon City 1101, Philippines
3Academic Production, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan

Received 7 November 2011; Accepted 3 December 2011

Academic Editors: M. Coppens, A. Morozov, and M. Visinescu

Copyright © 2012 Shyamal Kumar Hui and Richard S. Lemence. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. C. Chaki and R. K. Maity, “On quasi Einstein manifolds,” Publicationes Mathematicae Debrecen, vol. 57, no. 3-4, pp. 297–306, 2000. View at Zentralblatt MATH
  2. F. Defever, R. Deszcz, M. Hotloś, M. Kucharski, and Z. Sentürk, “Generalisations of Robertson-Walker spaces,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, vol. 43, pp. 13–24, 2000. View at Zentralblatt MATH
  3. R. Deszcz, F. Dillen, L. Verstraelen, and L. Vrancken, “Quasi-Einstein totally real submanifolds of S6(1),” The Tohoku Mathematical Journal, vol. 51, no. 4, pp. 461–478, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  4. R. Deszcz and M. Głogowska, “Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces,” Colloquium Mathematicum, vol. 94, no. 1, pp. 87–101, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. Deszcz, M. Głogowska, M. Hotloś, and Z. Sentürk, “On certain quasi-Einstein semisymmetric hypersurfaces,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, vol. 41, pp. 151–164, 1998. View at Zentralblatt MATH
  6. R. Deszcz and M. Hotloś, “On some pseudosymmetry type curvature condition,” Tsukuba Journal of Mathematics, vol. 27, no. 1, pp. 13–30, 2003. View at Zentralblatt MATH
  7. R. Deszcz and M. Hotloś, “On hypersurfaces with type number two in space forms,” Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, vol. 46, pp. 19–34, 2003. View at Zentralblatt MATH
  8. R. Deszcz, M. Hotloś, and Z. Sentürk, “Quasi-Einstein hypersurfaces in semi-Riemannian space forms,” Colloquium Mathematicum, vol. 89, no. 1, pp. 81–97, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. R. Deszcz, M. Hotloś, and Z. Sentürk, “On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces,” Soochow Journal of Mathematics, vol. 27, no. 4, pp. 375–389, 2001. View at Zentralblatt MATH
  10. R. Deszcz, P. Verheyen, and L. Verstraelen, “On some generalized Einstein metric conditions,” Institut Mathématique. Publications. Nouvelle Série, vol. 60, pp. 108–120, 1996. View at Zentralblatt MATH
  11. M. Głogowska, “Semi-Riemannian manifolds whose Weyl tensor is a Kulkarni-Nomizu square,” Institut Mathématique. Publications. Nouvelle Série, vol. 72, pp. 95–106, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. M. Głogowska, “On quasi-Einstein Cartan type hypersurfaces,” Journal of Geometry and Physics, vol. 58, no. 5, pp. 599–614, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. U. C. De and G. C. Ghosh, “On quasi Einstein manifolds,” Periodica Mathematica Hungarica, vol. 48, no. 1-2, pp. 223–231, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. A. A. Shaikh, D. W. Yoon, and S. K. Hui, “On quasi-Einstein spacetimes,” Tsukuba Journal of Mathematics, vol. 33, no. 2, pp. 305–326, 2009. View at Zentralblatt MATH
  15. A. A. Shaikh and A. Patra, “On quasi-conformally flat quasi-Einstein spaces,” Differential Geometry—Dynamical Systems, vol. 12, pp. 201–212, 2010. View at Zentralblatt MATH
  16. M. C. Chaki, “On generalized quasi Einstein manifolds,” Publicationes Mathematicae Debrecen, vol. 58, no. 4, pp. 683–691, 2001. View at Zentralblatt MATH
  17. M. C. Chaki, “On super quasi Einstein manifolds,” Publicationes Mathematicae Debrecen, vol. 64, no. 3-4, pp. 481–488, 2004. View at Zentralblatt MATH
  18. P. Debnath and A. Konar, “On super quasi Einstein manifold,” Institut Mathématique. Publications. Nouvelle Série, vol. 89, no. 103, pp. 95–104, 2011. View at Publisher · View at Google Scholar
  19. C. Özgür, “On some classes of super quasi-Einstein manifolds,” Chaos, Solitons and Fractals, vol. 40, no. 3, pp. 1156–1161, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. G. P. Pokhariyal and R. S. Mishra, “Curvature tensors' and their relativistics significance,” Yokohama Mathematical Journal, vol. 18, pp. 105–108, 1970. View at Zentralblatt MATH
  21. G. P. Pokhariyal and R. S. Mishra, “Curvature tensors and their relativistic significance. II,” Yokohama Mathematical Journal, vol. 19, no. 2, pp. 97–103, 1971. View at Zentralblatt MATH
  22. G. P. Pokhariyal, “Curvature tensors and their relativistic significance. III,” Yokohama Mathematical Journal, vol. 21, pp. 115–119, 1973. View at Zentralblatt MATH
  23. G. P. Pokhariyal, “Relativistic significance of curvature tensors,” International Journal of Mathematics and Mathematical Sciences, vol. 5, no. 1, pp. 133–139, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. G. P. Pokhariyal, “Curvature tensors on A-Einstein Sasakian manifolds,” Balkan Journal of Geometry and Its Applications, vol. 6, no. 1, pp. 45–50, 2001.
  25. U. C. De and A. Sarkar, “On a type of P-Sasakian manifolds,” Mathematical Reports, vol. 11, no. 2, pp. 139–144, 2009. View at Zentralblatt MATH
  26. K. Matsumoto, S. Ianuş, and I. Mihai, “On P-Sasakian manifolds which admit certain tensor fields,” Publicationes Mathematicae Debrecen, vol. 33, no. 3-4, pp. 199–204, 1986.
  27. G. P. Pokhariyal, “Study of a new curvature tensor in a Sasakian manifold,” The Tensor Society. Tensor. New Series, vol. 36, no. 2, pp. 222–226, 1982. View at Zentralblatt MATH
  28. A. A. Shaikh, S. K. Jana, and S. Eyasmin, “On weakly W2-symmetric manifolds,” Sarajevo Journal of Mathematics, vol. 3, no. 1, pp. 73–91, 2007. View at Zentralblatt MATH
  29. A. A. Shaikh, Y. Matsuyama, and S. K. Jana, “On a type of general relativistic spacetime with W2-curvature tensor,” Indian Journal of Mathematics, vol. 50, no. 1, pp. 53–62, 2008.
  30. A. Taleshian and A. A. Hosseinzadeh, “On W2-curvature tensor N(k)-quasi Einstein manifolds,” The Journal of Mathematics and Computer Science, vol. 1, no. 1, pp. 28–32, 2010.
  31. M. M. Tripathi and P. Gupta, “On τ-curvature tensor in K-contact and Sasakian manifolds,” International Electronic Journal of Geometry, vol. 4, no. 1, pp. 32–47, 2011.
  32. Venkatesha, C. S. Bagewadi, and K. T. Pradeep Kumar, “Some results on Lorentzian Para-Sasakian manifolds,” ISRN Geometry, vol. 2011, Article ID 161523, 9 pages, 2011. View at Publisher · View at Google Scholar
  33. A. Yíldíz and U. C. De, “On a type of Kenmotsu manifolds,” Differential Geometry—Dynamical Systems, vol. 12, pp. 289–298, 2010. View at Zentralblatt MATH
  34. F. Özen and S. Altay, “On weakly and pseudo-symmetric Riemannian spaces,” Indian Journal of Pure and Applied Mathematics, vol. 33, no. 10, pp. 1477–1488, 2002. View at Zentralblatt MATH
  35. F. Özen and S. Altay, “On weakly and pseudo concircular symmetric structures on a Riemannian manifold,” Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 47, pp. 129–138, 2008. View at Zentralblatt MATH
  36. A. A. Shaikh, I. Roy, and S. K. Hui, “On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces,” Global Journal Science Frontier Research, vol. 10, no. 4, pp. 28–30, 2010.
  37. D. Ferus, A Remark on Codazzi Tensors on Constant Curvature Space, vol. 838 of Lecture Notes in Mathematics, Global Differential Geometry and Global Analysis, Springer, New York, NY, USA, 1981.
  38. J. A. Schouten, Ricci-Calculus. An Introduction to Tensor Analysis and Its Geometrical Applications, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete, Bd X, Springer, Berlin, Germany, 1954.
  39. N. J. Hicks, Notes on Differential Geometry, Affiliated East West Press, 1969.
  40. B.-Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, NY, USA, 1973.
  41. L. P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, NJ, USA, 1949.