SUBMERSION FROM SEMI-RIEMANNIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

Abstract

In this paper, we introduce the idea of a lightlike submersion from a semi-Riemannian manifold onto a lightlike manifold, and give some examples. Then we define O’Neill’s tensors for such submersions and investigate their main properties. We show that the Schouten connection is not a metric connection in a lightlike submersion. We also investigate curvature properties of the manifolds and establish a relation between the null sectional curvatures of a semi-Riemannian manifold and a lightlike manifold.

Keywords

• Lightlike Manifold,Submersion,Lightlike submersion,2000 AMS Classification: 53 C 20

SUBMERSION FROM SEMI-RIEMANNIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

Abstract

References

1. Beem, J. K., Ehrlich, P. E. and Easley, K. L. Global Lorentzian geometry (Pure and Applied Mathematics 202, Marcel Dekker, Inc., New York, 1996).
2. Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi - Riemannian Manifolds and Applications(Kluwer Acad. Publishers, Dordrecht, 1996).
3. Gray, A. Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715–737, 1967.
4. Falcitelli, M., Ianus, S. and Pastore, A. M. Riemannian Submersions and Related Topics (World Scientific, 2004).
5. Kupeli, D. N. Singular Semi-Riemannian Geometry (Kluwer Dortrecht, 1996).
6. Nomizu, K. Fundamentals of Linear Algebra (McGraw Hill, New York, 1966).
7. O’Neill, B. The fundamental equations of a submersion, Michigan Math. J. 13, 459ˆu-469, 1966.
8. O’Neill, B. Semi-Riemannian Geometry with Application to Relativity (Academic Press, New York, 1983).

9. S¸ahin, B. On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds, Mediterranean J. Math. 5, 273–284, 2008.