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Year 2019, Volume: 2 Issue: 2, 104 - 109, 25.11.2019

Amith Kumar Debnath Sanjib Kumar Jana Fusun Nurcan , Joydeep Sengupta

Abstract

References

  • [1] M. C. Chaki, R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306.
  • [2] F. Defever, R. Deszcz, M. Hotlos, M. Kucharski, Z. Senturk, Generalisations of Robertson-Walker spaces, Annales Univ. Sci. Budapest. Eotvos Sect. Math., 43 (2000), 13-24.
  • [3] R. Deszcz, M. Hotlos, On some pseudosymmetry type curvature condition, Tsukuba J. Math., 27 (2003), 13-30.
  • [4] R. Deszcz, M. Hotlos, Z. Senturk, Quasi-Einstein hypersurfaces in semi-Riemannian space forms, Colloq. Math., 81 (2001), 81-97.
  • [5] R. Deszcz, M. Hotlos, Z. Senturk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math., 27(4) (2001), 375-389.
  • [6] R. DESZCZ, VERHEYEN, P. and VERSTRAELEN, L.: On some generalized Einstein metric conditions, Publ. Inst. Math. (Beograd), 60:74 (1996), pp. 108-120.
  • [7] S. K. Jana, A. K. Debnath, J. Sengupta: On Riemannian manifolds satisfying certain curvature conditions, Bulletin of Natural and Mathematical Sciences, Russia, 30(2) (2013), 40-61.
  • [8] A. Z. Petrov, Einstein Spaces, Pergamon Press, Oxford, 1949.
  • [9] L. Tamassy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Rimannian manifolds, Coll. Math. Soc., J. Bolyai 50 (1989), 663-670 .

On Quasi-Einstein Manifolds Admitting Space-Matter Tensor

Year 2019, Volume: 2 Issue: 2, 104 - 109, 25.11.2019

Amith Kumar Debnath Sanjib Kumar Jana Fusun Nurcan , Joydeep Sengupta

Abstract

The subject matter of this paper lies in the interesting domain of Differential Geometry and the Theory of General Relativity. Although the space has its motivation in Relativity, we study the geometric properties of the space, inspired by the papers on the geometry related to curvature restrictions. Such a study was joined by A. Z. Petrov to Einstein spaces. We extend the study on quasi-Einstein spaces which can be considered as a generalization of Einstein spaces. This study is supported by an example.

Keywords

Space-matter tensor Einstein's field equation scalar curvature Quasi-Einstein Manifolds

References

  • [1] M. C. Chaki, R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297-306.
  • [2] F. Defever, R. Deszcz, M. Hotlos, M. Kucharski, Z. Senturk, Generalisations of Robertson-Walker spaces, Annales Univ. Sci. Budapest. Eotvos Sect. Math., 43 (2000), 13-24.
  • [3] R. Deszcz, M. Hotlos, On some pseudosymmetry type curvature condition, Tsukuba J. Math., 27 (2003), 13-30.
  • [4] R. Deszcz, M. Hotlos, Z. Senturk, Quasi-Einstein hypersurfaces in semi-Riemannian space forms, Colloq. Math., 81 (2001), 81-97.
  • [5] R. Deszcz, M. Hotlos, Z. Senturk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math., 27(4) (2001), 375-389.
  • [6] R. DESZCZ, VERHEYEN, P. and VERSTRAELEN, L.: On some generalized Einstein metric conditions, Publ. Inst. Math. (Beograd), 60:74 (1996), pp. 108-120.
  • [7] S. K. Jana, A. K. Debnath, J. Sengupta: On Riemannian manifolds satisfying certain curvature conditions, Bulletin of Natural and Mathematical Sciences, Russia, 30(2) (2013), 40-61.
  • [8] A. Z. Petrov, Einstein Spaces, Pergamon Press, Oxford, 1949.
  • [9] L. Tamassy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Rimannian manifolds, Coll. Math. Soc., J. Bolyai 50 (1989), 663-670 .
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Conference Paper
Authors

Amith Kumar Debnath This is me 0000-0001-5398-1955

Sanjib Kumar Jana This is me 0000-0002-4221-8249

Fusun Nurcan 0000-0003-0146-992X

Joydeep Sengupta This is me 0000-0002-1609-0798

Acceptance Date October 8, 2019
Publication Date November 25, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Debnath, A. K., Jana, S. K., Nurcan, F., Sengupta, J. (2019). On Quasi-Einstein Manifolds Admitting Space-Matter Tensor. Conference Proceedings of Science and Technology, 2(2), 104-109.
AMA Debnath AK, Jana SK, Nurcan F, Sengupta J. On Quasi-Einstein Manifolds Admitting Space-Matter Tensor. Conference Proceedings of Science and Technology. November 2019;2(2):104-109.
Chicago Debnath, Amith Kumar, Sanjib Kumar Jana, Fusun Nurcan, and Joydeep Sengupta. “On Quasi-Einstein Manifolds Admitting Space-Matter Tensor”. Conference Proceedings of Science and Technology 2, no. 2 (November 2019): 104-9.
EndNote Debnath AK, Jana SK, Nurcan F, Sengupta J (November 1, 2019) On Quasi-Einstein Manifolds Admitting Space-Matter Tensor. Conference Proceedings of Science and Technology 2 2 104–109.
IEEE A. K. Debnath, S. K. Jana, F. Nurcan, and J. Sengupta, “On Quasi-Einstein Manifolds Admitting Space-Matter Tensor”, Conference Proceedings of Science and Technology, vol. 2, no. 2, pp. 104–109, 2019.
ISNAD Debnath, Amith Kumar et al. “On Quasi-Einstein Manifolds Admitting Space-Matter Tensor”. Conference Proceedings of Science and Technology 2/2 (November2019), 104-109.
JAMA Debnath AK, Jana SK, Nurcan F, Sengupta J. On Quasi-Einstein Manifolds Admitting Space-Matter Tensor. Conference Proceedings of Science and Technology. 2019;2:104–109.
MLA Debnath, Amith Kumar et al. “On Quasi-Einstein Manifolds Admitting Space-Matter Tensor”. Conference Proceedings of Science and Technology, vol. 2, no. 2, 2019, pp. 104-9.
Vancouver Debnath AK, Jana SK, Nurcan F, Sengupta J. On Quasi-Einstein Manifolds Admitting Space-Matter Tensor. Conference Proceedings of Science and Technology. 2019;2(2):104-9.