Research Article
BibTex RIS Cite

CR-Submanifolds of Lorentzian Manifolds

Year 2009, Volume: 2 Issue: 1, 95 - 103, 30.04.2009

Pablo Alegre

Abstract


Keywords

Lorentzian metric contact and almost contact Lorentzian manifolds Lorentzian Sasakian Lorentzian Sasakian space form generalized Lorentzian Sasakian space form invariant anti-invariant and CR-submanifolds

References

  • [1] Alegre, P., CR-submanifolds of normal Lorentzian Sasakian manifolds, Submitted.
  • [2] Alegre, P. and Carriazo, A., Lorentzian Sasakian manifolds with constant pointwise φ- sectional curvature, Submitted.
  • [3] Alegre, P., Blair, D.E. and Carriazo, A., Generalized Sasakian-space-forms, Israel J. Math., 141(2004), 157-183.
  • [4] Barros, M. and Urbano, F., CR-submanifolds of generalized complex space forms, An. S»ti. Univ.“Al. I. Cuza” Iasi Sect. I a Mat., 25(1979), no. 2, 355-363.
  • [5] Bejancu, A., CR-submanifolds of a Kaehler manifold. I., Proc. Amer. Math. Soc., 69(1978), no. 1, 135-142.
  • [6] Bejancu, A. and Papaghiuc, N., Semi-invariant submanifolds of a Sasakian manifold, An. S»ti. Univ. .“Al. I. Cuza” Iasi Sect. I a Mat., 27, s.1 (1981), 163-170.
  • [7] Bejancu, A. and Papaghiuc, N., Semi-invariant submanifolds of a Sasakian space form, Colloq. Math., 48(1984), 77-88.
  • [8] Blair, D.E. and Chen, B.Y., On CR-submanifolds of Hermitian manifolds, Israel J. Math., 34(1979), no. 4, 353-363.
  • [9] Cabrerizo, J.L., Carriazo, A., Fernandez, L.M. and Fernandez, M., Semi-Slant submanifolds in Sasakian manifolds, Geometriae Dedicata, 78(1999), 183-199.
  • [10] Gill, H. and Dube, K.K., Generalized CR-submanifolds of the trans hyperbolic Sasakian manifold, Demonstratio Math., 38, no.4, (2005), 953-960.
  • [11] Gill, H. and Dube, K.K., Generalized CR-submanifolds of a trans Lorentzian para Sasakian manifold, Proc. Natl. Acad. Sci. India Sect. A, 76(A), II, (2006), 119-124.
  • [12] Kalpana and Guha, G., Semi-invariant submanifold of a Lorentzian para-Sasakian manifold, Ganit, 13(1993), no. 1-2, 71-76.
  • [13] Ikawa, T., Spacelike maximal surfaces with constant scalar normal curvature in a normal contact Lorentzian manifold, Bull. Malaysian Math. Soc., 21(1998), 31-36.
  • [14] Kobayashi, M., CR submanifolds of a Sasakian manifold, Tensor (N.S.), 35, no. 3, 297-307.
  • [15] Papaghiuc, N., Almost semi-invariant submanifolds in Sasakian Space forms, An. şt. Univ. Iaşi.,29(1983), 5-10.
  • [16] Papaghiuc, N., Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Şti. Univ. “Al. I. Cuza” Iasi Sect. I a Mat., 32(1986), 73-76.
  • [17] Ronsse, G.S., Generic and skew CR submanifolds of a Kaehler manifold, Bull. Inst. Math. Acad. Sinica, 18(1990), no. 2, 127-141.
  • [18] Tripathi, M.M., Some characterizations of CR-submanifolds of generalized complex space forms, Kuwait J. Sci. Engrg., 23(1996), no. 2, 133-138.

Year 2009, Volume: 2 Issue: 1, 95 - 103, 30.04.2009

Pablo Alegre

Abstract

References

  • [1] Alegre, P., CR-submanifolds of normal Lorentzian Sasakian manifolds, Submitted.
  • [2] Alegre, P. and Carriazo, A., Lorentzian Sasakian manifolds with constant pointwise φ- sectional curvature, Submitted.
  • [3] Alegre, P., Blair, D.E. and Carriazo, A., Generalized Sasakian-space-forms, Israel J. Math., 141(2004), 157-183.
  • [4] Barros, M. and Urbano, F., CR-submanifolds of generalized complex space forms, An. S»ti. Univ.“Al. I. Cuza” Iasi Sect. I a Mat., 25(1979), no. 2, 355-363.
  • [5] Bejancu, A., CR-submanifolds of a Kaehler manifold. I., Proc. Amer. Math. Soc., 69(1978), no. 1, 135-142.
  • [6] Bejancu, A. and Papaghiuc, N., Semi-invariant submanifolds of a Sasakian manifold, An. S»ti. Univ. .“Al. I. Cuza” Iasi Sect. I a Mat., 27, s.1 (1981), 163-170.
  • [7] Bejancu, A. and Papaghiuc, N., Semi-invariant submanifolds of a Sasakian space form, Colloq. Math., 48(1984), 77-88.
  • [8] Blair, D.E. and Chen, B.Y., On CR-submanifolds of Hermitian manifolds, Israel J. Math., 34(1979), no. 4, 353-363.
  • [9] Cabrerizo, J.L., Carriazo, A., Fernandez, L.M. and Fernandez, M., Semi-Slant submanifolds in Sasakian manifolds, Geometriae Dedicata, 78(1999), 183-199.
  • [10] Gill, H. and Dube, K.K., Generalized CR-submanifolds of the trans hyperbolic Sasakian manifold, Demonstratio Math., 38, no.4, (2005), 953-960.
  • [11] Gill, H. and Dube, K.K., Generalized CR-submanifolds of a trans Lorentzian para Sasakian manifold, Proc. Natl. Acad. Sci. India Sect. A, 76(A), II, (2006), 119-124.
  • [12] Kalpana and Guha, G., Semi-invariant submanifold of a Lorentzian para-Sasakian manifold, Ganit, 13(1993), no. 1-2, 71-76.
  • [13] Ikawa, T., Spacelike maximal surfaces with constant scalar normal curvature in a normal contact Lorentzian manifold, Bull. Malaysian Math. Soc., 21(1998), 31-36.
  • [14] Kobayashi, M., CR submanifolds of a Sasakian manifold, Tensor (N.S.), 35, no. 3, 297-307.
  • [15] Papaghiuc, N., Almost semi-invariant submanifolds in Sasakian Space forms, An. şt. Univ. Iaşi.,29(1983), 5-10.
  • [16] Papaghiuc, N., Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Şti. Univ. “Al. I. Cuza” Iasi Sect. I a Mat., 32(1986), 73-76.
  • [17] Ronsse, G.S., Generic and skew CR submanifolds of a Kaehler manifold, Bull. Inst. Math. Acad. Sinica, 18(1990), no. 2, 127-141.
  • [18] Tripathi, M.M., Some characterizations of CR-submanifolds of generalized complex space forms, Kuwait J. Sci. Engrg., 23(1996), no. 2, 133-138.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Pablo Alegre

Publication Date April 30, 2009
Published in Issue Year 2009 Volume: 2 Issue: 1

Cite

APA Alegre, P. (2009). CR-Submanifolds of Lorentzian Manifolds. International Electronic Journal of Geometry, 2(1), 95-103.
AMA Alegre P. CR-Submanifolds of Lorentzian Manifolds. Int. Electron. J. Geom. April 2009;2(1):95-103.
Chicago Alegre, Pablo. “CR-Submanifolds of Lorentzian Manifolds”. International Electronic Journal of Geometry 2, no. 1 (April 2009): 95-103.
EndNote Alegre P (April 1, 2009) CR-Submanifolds of Lorentzian Manifolds. International Electronic Journal of Geometry 2 1 95–103.
IEEE P. Alegre, “CR-Submanifolds of Lorentzian Manifolds”, Int. Electron. J. Geom., vol. 2, no. 1, pp. 95–103, 2009.
ISNAD Alegre, Pablo. “CR-Submanifolds of Lorentzian Manifolds”. International Electronic Journal of Geometry 2/1 (April 2009), 95-103.
JAMA Alegre P. CR-Submanifolds of Lorentzian Manifolds. Int. Electron. J. Geom. 2009;2:95–103.
MLA Alegre, Pablo. “CR-Submanifolds of Lorentzian Manifolds”. International Electronic Journal of Geometry, vol. 2, no. 1, 2009, pp. 95-103.
Vancouver Alegre P. CR-Submanifolds of Lorentzian Manifolds. Int. Electron. J. Geom. 2009;2(1):95-103.