DOI QR코드

DOI QR Code

TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

  • Jin, Dae-Ho (Department of Mathematics, Dongguk University)
  • Received : 2010.10.11
  • Accepted : 2011.02.16
  • Published : 2011.02.28

Abstract

In this paper, we study the geometry of transversal half lightlike sub-manifolds of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a transversal half lightlike submanifold. In addition to these main theorems, we study the geometry of totally umbilical transversal half lightlike submanifolds of an indefinite Sasakian manifold.

Keywords

References

  1. Atindogbe, C. & Duggal, K.L.: Conformal screen on light like hypersurfaces. International J. of Pure and Applied Math. 11 (2004), no. 4., 421-442.
  2. Duggal, K.L. & Bejancu, A.: Lightlike submanifolds of codimension 2. Math. J. Toyama Univ. 15 (1992), 59-82.
  3. Duggal, K.L. & Bejancu, A.: Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications. Kluwer Acad. Publishers, Dordrecht, 1996.
  4. Duggal, K.L. & Jin, D.H.: Half-Lightlike Submanifolds of Codimension 2. Math. J. Toyama Univ. 22 (1999), 121-161.
  5. Duggal, K.L. & Jin, D.H.: Null curves and Hypersurfaces of Semi-Riemannian Manifolds. World Scientific, 2007.
  6. Duggal, K.L. & Sahin, B.: Generalized Cauchy-Riemann lightlike Submanifolds of indefinite Sasakian manifolds. Acta Math. Hungar. 112 (2006), no. 1-2., 113-136.
  7. Duggal, K.L. & Sahin, B.: Lightlike Submanifolds of indefinite Sasakian manifolds. Int. J. Math. and Math. Sci., 2007, Art ID 57585, 1-21.
  8. Jin, D.H.: Geometry of screen conformal real half lightlike submanifolds. Bull. Korean Math. Soc. 47 (2010), no. 4., 701-714. https://doi.org/10.4134/BKMS.2010.47.4.701
  9. Jin, D.H.: Real half lightlike submanifolds with totally umbilical properties. J. Korea Soc Math. Edu. 17 (2010), no. 1., 51-63.
  10. Jin, D.H.: Half lightlike submanifolds with totally umbilical screen distributions J. Korea Soc. Math. Edu. 17 (2010), no. 1., 29-38.
  11. Jin, D.H.: Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. Indian J. Pure and Appl. Math. 41 (2010), no. 4., 569-581. https://doi.org/10.1007/s13226-010-0032-y
  12. Kang, T.H., Jung, S.D., Kim, B.H., Pak, H.K. & Pak, J.S.: Lightlike hypersurfaces of indefinite Sasakian manifolds. Indian J. Pure and Appl. Math. 34 (2003), 1369-1380.
  13. Kupeli, D. N., Singular Semi-Riemannian Geometry, Mathematics and Its Applications, Kluwer Acad. Publishers, Dordrecht, 1996.
  14. Yano, K., Eum, S.S. & Ki, U.H.: On transversal hypersurfaces of an almost contact manifold Kodai Math. Sem. Rep. 24, 1972, 459-470. https://doi.org/10.2996/kmj/1138846638

Cited by

  1. SPECIAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD vol.29, pp.1, 2014, https://doi.org/10.4134/CKMS.2014.29.1.109
  2. ASCREEN LIGHTLIKE HYPERSURFACES OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION vol.29, pp.2, 2014, https://doi.org/10.4134/CKMS.2014.29.2.311
  3. INDEFINITE TRANS-SASAKIAN MANIFOLD ADMITTING AN ASCREEN HALF LIGHTLIKE SUBMANIFOLD vol.29, pp.3, 2014, https://doi.org/10.4134/CKMS.2014.29.3.451
  4. HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD vol.51, pp.4, 2014, https://doi.org/10.4134/BKMS.2014.51.4.979
  5. INDEFINITE GENERALIZED SASAKIAN SPACE FORM ADMITTING A GENERIC LIGHTLIKE SUBMANIFOLD vol.51, pp.6, 2014, https://doi.org/10.4134/BKMS.2014.51.6.1711
  6. NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC 𝜃-CONNECTIONS vol.30, pp.1, 2015, https://doi.org/10.4134/CKMS.2015.30.1.035
  7. NON-TANGENTIAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE COSYMPLECTIC MANIFOLD vol.20, pp.2, 2013, https://doi.org/10.7468/jksmeb.2013.20.2.89