DOI QR코드

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ON SOME PROPERTIES OF SEMI-INVARIANT SUBMANIFOLDS OF A NEARLY TRANS-SASAKIAN MANIFOLD ADMITTING A QUARTER-SYMMETRIC NON-METRIC CONNECTION

  • 발행 : 2012.02.15

초록

We define a quarter-symmetric non-metric connection in a nearly trans-Sasakian manifold and we consider semi-invariant submanifolds of a nearly trans-Sasakian manifold endowed with a quarter-symmetric non-metric connection. Moreover, we also obtain integrability conditions of the distributions on semi-invariant submanifolds.

키워드

참고문헌

  1. M. Ahmad, Semi-invariant submanifolds of nearly Kenmotsu manifold with the canonical semi-symmetric semi-metric connection, Mathematicki Vesnik 62 (2010), 189-198.
  2. M. Ahmad, J. B. Jun, and A. Haseeb, Hypersurfaces of almost r-paracontact Riemannian manifold endowed with quarter-symmetric metric connection, Bull. Korean Math. Soc. 46 (2009), no. 3, 477-487. https://doi.org/10.4134/BKMS.2009.46.3.477
  3. M. Ahmad, C. Ozgur, and A. Haseeb, Hypersurfaces of almost r-paracontact Riemannian manifold endowed with quarter-symmetric non-metric connection, Kyungpook Math. J. 49 (2009), 533-543. https://doi.org/10.5666/KMJ.2009.49.3.533
  4. M. Ahmad, S. Rahman, and M. D. Siddiqi, Semi-invariant submanifolds of a nearly Sasakian manifold endowed with a semi-symmetric metric connection, Bull. Allahabad Math. Soc. 25, part 1(2010), 23-33.
  5. A. Bejancu, On semi-invariant submanifold of an almost contact metric manifold, A. Stiint. Univ. "AL .I. Cuza" Iasi Mat. 27(supplement)(1981), 17-21.
  6. A. Bejancu,Geometry of CR-submanifolds, D. Reidel publishing company, Holland, 1986.
  7. D. E. Blair, Contact manifold in Riemannian geometry, Lecture Notes in Math. 509, Springer Verlag 1976.
  8. L. S. Das and M. Ahmad, CR-Submanifolds of LP-Sasakian manifold with quarter-symmetric non-metric connection, Math. Sci. Res. J. 13(7)(2009), 161- 169.
  9. L. S. Das, R. Nivas, S. Ali, and M. Ahmad, Study of submanifolds immersed in a manifold with quarter-symmetric semi-metric connection, Tensor N. S. 65 (2004), 250-260.
  10. C. Gherghe, Harmonicity on nearly trans-Sasaki manifolds, Demostratio. Math. 33 (2000), 151-157.
  11. S. Golab, On semi-symmetric and quarter-symmetric linear connections. Tensor N. S. 29 (1975), 249-254.
  12. D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), 1-27. https://doi.org/10.2996/kmj/1138036310
  13. M. Kobayashi, Semi-invariant submanifold of a certain class of almost contact manifolds, Tensor 43 (1986), 28-36.
  14. J. C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl. (4), 162(1992), 77-86.
  15. R. Nivas and G. Verma, On quarter-symmetric non-metric connection in a Riemannian manifold, J. Rajasthan Acad. Sci. 4 (2005), no. 1, 57-68.
  16. J. A. Oubina, New Class of almost contact metric structures, Publ. Math. Debrecen 32 (1985), 187-193.
  17. S. N. Pandey, and R. S. Mishra, On quarter-symmetric metric F-connections, Tensor 34 (1980), 1-7.
  18. M. H. Shahid, CR-Submanifolds of trans-Sasakian manifold, Indian J. Pure Appl. Math. 22 (1991), 1007-1012.

피인용 문헌

  1. η-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION vol.42, pp.3, 2012, https://doi.org/10.5831/hmj.2020.42.3.601