DOI QR코드

DOI QR Code

SEMI-INVARIANT SUBMANIFOLDS OF (LCS)n-MANIFOLD

  • Received : 2017.09.26
  • Accepted : 2017.11.30
  • Published : 2018.10.31

Abstract

In this paper the decomposition of basic equations of $(LCS)_n$-manifolds is carried out into horizontal and vertical projections. Further, we study the integrability of the distributions $D,D{\oplus}[{\xi}]$ and $D^{\perp}$ totally geodesic of semi-invariant submanifolds of $(LCS)_n$-manifold.

Keywords

References

  1. C. S. Bagewadi, D. Nirmala, and M. S. Siddesha, Semi-invariant submanifolds of (k, ${\mu}$)- contact manifold, Bull. Cal. Math. Soc. 109 (2017), no. 2, 93-100.
  2. A. Bejancu, Geometry of CR-Submanifolds, Mathematics and its Applications (East European Series), 23, D. Reidel Publishing Co., Dordrecht, 1986.
  3. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509, Springer-Verlag, Berlin, 1976.
  4. L. S. Das, Mobin Ahmad, M. Danish Siddiqi, and A. Haseeb, On semi-invariant submanifolds of a nearly trans-Sasakian manifold admitting a semi-symmetric semi-metric connection, Demonstratio Math. 46 (2013), no. 2, 345-359. https://doi.org/10.1515/dema-2013-0447
  5. A. De, A note on invariant submanifolds of (k, ${\mu}$)-contact manifolds, Ukrainian Math. J. 62 (2011), no. 11, 1803-1809. https://doi.org/10.1007/s11253-011-0469-0
  6. S. IanuIanuIanu and I. Mihai, Semi-invariant submanifolds of an almost paracontact manifold, Tensor (N.S.) 39 (1982), 195-200.
  7. M. Kobayashi, On semi-invariant submanifolds of S-manifolds of constant f-sectional curvature, Tensor (N.S.) 51 (1992), no. 1, 41-47.
  8. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12 (1989), no. 2, 151-156.
  9. B. Prasad, Semi-invariant submanifolds of a Lorentzian para-Sasakian manifold, Bull. Malaysian Math. Soc. (2) 21 (1998), no. 1, 21-26.
  10. V. S. Prasad and C. S. Bagewadi, Semi-invariant submanifolds of Kenmotsu manifolds, Ganita 50 (1999), no. 1, 73-81.
  11. R. Prasad, S. Sharma, and A. K. Raj, Semi-invariant submanifolds of nearly transSasakian manifolds, Bull. of Mal. Mat. Sci. Soc. 98 (2006), no. 4, 347-366.
  12. A. A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J. 43 (2003), no. 2, 305-314.
  13. A. A. Shaikh and T. Q. Binh, On weakly symmetric $(LCS)_n$-manifolds, J. Adv. Math. Stud. 2 (2009), no. 2, 103-118.
  14. B. B. Sinha and A. K. Srivastava, Semi-invariant submanifolds of a Kenmotsu manifold with constant $\phi$-holomorphic sectional curvature, Indian J. Pure Appl. Math. 23 (1992), no. 11, 783-789.
  15. M. M. Tripathi, On semi-invariant submanifolds of LP-cosymplectic manifolds, Bulletin of the Malaysian Mathematical Sciences Society 24 (2001), 69-79.