African Diaspora Journal of Mathematics

Screen Conformal Invariant Light-like Hypersurfaces of Indefinite Sasakian Space Forms

F. Massamba

Full-text: Open access

Abstract

In this paper, we investigate a class of screen conformal invariant lightlike hypersurfaces of an indefinite Sasakian manifold. The geometric configuration of such hypersurfaces is established. We prove that its geometry is closely related to the one of leaves of its conformal screen distributions. We also prove that, in any leaf of a conformal screen distribution of an invariant lightlike hypersurface of an indefinite Sasakian space form, the parallelism and semiparallelism notions are equivalent.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 14, Number 2 (2012), 22-37.

Dates
First available in Project Euclid: 31 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1375293534

Mathematical Reviews number (MathSciNet)
MR3093232

Zentralblatt MATH identifier
1279.53044

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Indefinite Sasakian space form Lightlike hypersurface Screen conformal distribution

Citation

Massamba, F. Screen Conformal Invariant Light-like Hypersurfaces of Indefinite Sasakian Space Forms. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 2, 22--37. https://projecteuclid.org/euclid.adjm/1375293534


Export citation

References

  • D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics 203. Birkhauser Boston, Inc., Boston, MA, 2002.
  • A. Bejancu and K. L. Duggal, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications. Kluwer Publishers, 1996.
  • A. Bonome, R. Castro, E. García-Rio, L. Hervella, Curvature of indefinite almost contact manifolds, J. geom., 58 (1997), 66-86.
  • C. Calin, Contribution to geometry of $CR$-submanifold, Thesis, University of Iasi, Iasi, Romania, 1998.
  • K. L. Duggal, On scalar curvature in lightlike geometry, J. Geom. Phys., 57 (2007), no.2, 473-481.
  • K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics, 2010.
  • D. N. Kupeli, Singular semi-invariant geometry, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  • S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Spacetime, Cambridge Univ. Press, Cambridge, 1972.
  • S. Maclane, Geometrical mechanics II, Lecture Notes, University of Chicago, Chicago, III, USA 1968.
  • F. Massamba, Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, Kodai Math. J., 31 (2008), 338-358.
  • F. Massamba, $\eta$-totally umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, Contemporary problems in mathematical physics, 269-279, Int. Chair Math. Phys. Appl. (ICMPA-UNESCO Chairs), Cotonou, 2008.
  • F. Massamba, Lightlike hypersurfaces of indefinite Sasakian manifolds with parallel symmetric bilinear forms, Differ. Geom. Dyn. Syst., 10 (2008), 226-234.
  • F. Massamba, Screen integrable lightlike hypersurfaces of indefinite Sasakian manifolds, Mediterr. J. Math., 6 (2009), 27-46.
  • F. Massamba, Semi-parallel lightlike hypersurfaces of indefinite Sasakian manifolds, Int. J. Contemp. Math. Sci., 3 (2008), no.13-16, 629-634.
  • V. E. Nazaikinskii, V. E. Shatalov and B. Y. Sternin, Contact geometry and linear differential equations, Walter de Gruyter, Berlin, Germany 1992.
  • B.O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Mathematics, Academic Press, New York, 1983.
  • T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 271-290.
  • K. Yano and M. Kon, Structures on manifolds, Ser. Pure Math. 3 (Singapore: World Scientific), 1984.