대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제34권3호
  • /
  • Pages.921-934
  • /
  • 2019
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

ON A TYPE OF GENERALIZED SYMMETRIC MANIFOLDS

  • Kumar, Rajesh (Department of Mathematics Pachhunga University College)
  • 투고 : 2018.07.23
  • 심사 : 2018.12.13
  • 발행 : 2019.07.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The object of the present paper is to study generalized pseudo-projectively symmetric manifolds and Einstein generalized pseudo-projectively symmetric manifolds. Finally, the existence of generalized pseudo-projectively symmetric manifolds have been proved by two non-trivial examples.

키워드

참고문헌

  1. T. Adati and T. Miyazawa, On conformally symmetric spaces, Tensor (N.S.) 18 (1967), 335-342.
  2. A. L. Besse, Einstein Manifolds, Ergeb. Math. Grenzgeb. 3 Folge, Bd. 10, Springer-Verlag, Berlin, Heidelberg, New Yark, 1987.
  3. T. Q. Binh, On weakly symmetric Riemannian spaces, Publ. Math. Debrecen 42 (1993), no. 1-2, 103-107.
  4. E. Cartan, Sur une classe remarquable d'espaces de Riemann, Bull. Soc. Math. France 54 (1926), 214-264. https://doi.org/10.24033/bsmf.1105
  5. M. C. Chaki, On pseudo symmetric manifolds, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 33 (1987), no. 1, 53-58.
  6. M. C. Chaki and B. Gupta, On conformally symmetric spaces, Indian J. Math. 5 (1963), 113-122.
  7. A. De, On almost pseudo symmetric manifolds admitting a type of semi-symmetric non-metric connection, Acta Math. Hungar. 125 (2009), no. 1-2, 183-190. https://doi.org/10.1007/s10474-009-9002-4
  8. U. C. De and S. Bandyopadhyay, On weakly symmetric Riemannian spaces, Publ. Math. Debrecen 54 (1999), no. 3-4, 377-381.
  9. U. C. De and A. K. Gazi, On almost pseudo symmetric manifolds, Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 51 (2008), 53-68 (2009).
  10. U. C. De and A. K. Gazi, On almost pseudo conformally symmetric manifolds, Demonstratio Math. 42 (2009), no. 4, 869-886. https://doi.org/10.1515/dema-2009-0419
  11. U. C. De and A. K. Gazi, On conformally flat almost pseudo Ricci symmetric manifolds, Kyungpook Math. J. 49 (2009), no. 3, 507-520. https://doi.org/10.5666/KMJ.2009.49.3.507
  12. U. C. De and S. Mallick, On almost pseudo concircularly symmetric manifolds, J. Math. Computer Sci. 4 (2012), no. 3, 317-330. https://doi.org/10.22436/jmcs.04.03.05
  13. U. C. De and D. Tarafdar, On pseudo concircular symmetric manifolds, Bull. Calcutta Math. Soc. 84 (1992), no. 1, 77-80.
  14. P. Desai and K. Amur, On symmetric spaces, Tensor (N.S.) 29 (1975), no. 2, 119-124.
  15. R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), no. 3, 311-322.
  16. A. Derdzinski and W. Roter, Some theories of conformally symmetric manifolds, Tensor (N.S.) 32 (1978), no. 1, 11-23.
  17. E. G lodek, Some remarks on conformally symmetric Riemannian spaces, Colloq. Math. 23 (1971), 121-123. https://doi.org/10.4064/cm-23-1-121-123
  18. S. Guler and S. A. Demirbag, Riemannian manifolds satisfying certain conditions on pseudo-projective curvature tensor, Filomat 30 (2016), no. 3, 721-731. https://doi.org/10.2298/FIL1603721G
  19. S. K. Hui, Y. Matsuyama, and A. A. Shaikh, On decomposable weakly conformally symmetric manifolds, Acta Math. Hungar. 128 (2010), no. 1-2, 82-95. https://doi.org/10.1007/s10474-010-9158-y
  20. J. P. Jaiswal and R. H. Ojha, On weakly pseudo-projectively symmetric manifolds, Dier. Geom. Dyn. Syst. 12 (2010), 83-94.
  21. R. S. Mishra, Structures on a differentiable manifold and their applications, Chandrama Prakashan, Allahabad, 1984.
  22. B. O'Neill, Semi-Riemannian Geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983.
  23. B. Prasad, A pseudo projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 3, 163-166.
  24. A. A. Shaikh and S. K. Hui, On weakly projective symmetric manifolds, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 25 (2009), no. 2, 247-269.
  25. Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X, Y) . R = 0. I. The local version, J. Differential Geom. 17 (1982), no. 4, 531-582 (1983). http://projecteuclid.org/euclid.jdg/1214437486
  26. L. Tamassy and T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, in Differential geometry and its applications (Eger, 1989), 663-670, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992.
  27. S. V. Vishnuvardhana and Venkatesha, Almost pseudo symmetric Sasakian manifold admitting a type of quarter symmetric metric connection, Commun. Math. 23 (2015), no. 2, 163-169.
  28. Y. Wang and W. Wang, Curvature properties of almost Kenmotsu manifolds with generalized nullity conditions, Filomat 30 (2016), no. 14, 3807-3816. https://doi.org/10.2298/FIL1614807W
  29. K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, 3, World Scientic Publishing Co., Singapore, 1984.