한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제24권2호
  • /
  • Pages.53-68
  • /
  • 2017
  • /
  • 1226-0657(pISSN)
  • /
  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

ON GENERALIZED Z-RECURRENT MANIFOLDS

  • De, Uday Chand (Department of Pure Mathematics, University of Calcutta) ;
  • Pal, Prajjwal (Chakdaha Co-operative Colony Vidyayatan(H.S))
  • 투고 : 2014.12.04
  • 심사 : 2017.05.09
  • 발행 : 2017.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.

키워드

참고문헌

  1. T. Adati & T. Miyazawa: On a Riemannian space with recurrent conformal curvature. Tensor(N.S.) 18 (1967), 348-354.
  2. K. Arslan, U.C. De, C. Murathan & A. Yildiz: On generalized recurrent Riemannian manifolds. Acta Math. Hungarica 123 (2009), 27-39. https://doi.org/10.1007/s10474-008-8049-y
  3. E. Cartan: Sur une classes remarquable d'espaces de Riemannian. Bull. Soc. Math. France, 54 (1926), 214-264.
  4. M.C. Chaki: Some theorems on recurrent and Ricci-recurrent spaces. Rendiconti Seminario Math. Della Universita Di Padova 26 (1956), 168-176.
  5. M.C. Chaki & B. Gupta: On conformally symmetric spaces. Indian J. Math. 5 (1963), 113-122.
  6. M.C. Chaki: On pseudo symmetric manifolds. Ann. St. Univ. "Al I Cuza" Iasi 33 (1987), 53-58.
  7. M.C. Chaki: On pseudo Ricci symmetric manifolds. Bulg. J. Phys. 15 (1988), 525-531.
  8. M.C. Chaki & S.K. Saha: On pseudo-projective Ricci symmetric manifolds. Bulg. J. Phys. 21 (1994), 1-7.
  9. B.Y. Chen & K. Yano: Hypersurfaces of a conformally flat spaces. Tensor, N. S. 26 (1972), 318-322.
  10. S.S. Chern: On the curvature and characteristic classes of a Riemannian manifold. Abh. Math. Sem. Univ. Hamburg 20 (1956), 117-126.
  11. U.C. De & A.K. Gazi: On generalized concircularly recurrent manifolds. Studia Sci. Math. Hungar 46 (2009), no. 2, 287-296. https://doi.org/10.1556/SScMath.46.2009.2.1091
  12. U.C. De, N. Guha & D. Kamilya: On generalized Ricci-recurrent manifolds. Tensor(N.S.) 56 (1995), 312-317.
  13. L.P. Eisenhart: Riemannian Geometry. Princeton University Press, 1949.
  14. D. Ghosh: On projective recurrent spaces of second order. Acad. Roy. Belg. Bull. Cl. Sci. 56 (1970), no. 5, 1093-1099.
  15. A. Lichnerowicz: Courbure, nombres de Betti, et espaces symmetriques. Proc. Int. Cong. Math. 2 (1950), 216-233.
  16. S. Mallick, A. De & U.C. De: On generalized Ricci recurrent manifolds with applications to relativity. Proc. Nat. Acad. Sci., India, Sect. A Phys. Sci. 83 (2013), 143-152. https://doi.org/10.1007/s40010-013-0065-9
  17. C.A. Mantica & Y.J. Suh: Conformally symmetric manifolds and quasi-conformally recurrent Riemannian manifolds. Balkan J. Geom. Appl. 16 (2011), 66-67.
  18. C.A. Mantica & L.G. Molinari: Weakly Z-Symmetric manifolds. Acta Math. Hungarica 135 (2012), 80-96. https://doi.org/10.1007/s10474-011-0166-3
  19. C.A. Mantica & Y.J. Suh: Pseudo-Z-symmetric Riemannian manifolds with harmonic curvature tensors. Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250004(21 pages).
  20. C.A. Mantica & Y.J. Suh: Recurrent Z forms on Riemannian and Kaehler manifolds. Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250059(26 pages).
  21. B. O'Neill: Semi-Riemannian Geometry with Applications to the Relativity. Academic Press, New York-London, 1983.
  22. C. Ozgur: On generalized recurrent Kenmotsu manifolds. World Applied Sciences Journal 2 (2007), 9-33.
  23. C. Ozgur: On generalized recurrent contact metric manifolds Indian J. Math. 50 (2008), 11-19.
  24. C. Ozgur: On generalized recurrent Lorentzian para-Sasakian manifolds. Int. J. Appl. Math. Stat. 13 (2008), 92-97.
  25. E.M. Patterson: Some theorems on Ricci-recurrent spaces. J. London. Math. Soc. 27 (1952), 287-295.
  26. N. Prakash: A note on Ricci-recurrent and recurrent spaces. Bull. Cal. Math. Society 54 (1962), 1-7.
  27. W. Roter: On conformally symmetric Ricci-recurrent spaces. Colloquium Mathematicum. 31 (1974), 87-96. https://doi.org/10.4064/cm-31-1-87-96
  28. J.A. Schouten: Ricci-Calculus. An introduction to Tensor Analysis and its Geometrical Applications. Springer-Verlag, Berlin-Gottingen-Heidelberg, 1954.
  29. L. Tamassy & T.Q. Binh: On weakly symmetries of Einstein and Sasakian manifolds: Tensor (N.S.). 53 (1993), 140-148.
  30. A.G. Walker: On Ruse's space of recurrent curvature. Proc. of London Math. Soc., 52 (1950), 36-54.
  31. S. Yamaguchi & M. Matsumoto: On Ricci-recurrent spaces. Tensor, N. S. 19 (1968), 64-68.
  32. K. Yano & M. Kon: Structures on manifolds. World scientific, Singapore, 1984, 418-421.