SUBMERSION FROM SEMI-RIEMANNIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

Yıl 2010, Cilt: 39 Sayı: 1, 41 - 53, 01.01.2010

Bayram Sahin Yilmaz Gündüzalp

Öz

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.

Anahtar Kelimeler

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

SUBMERSION FROM SEMI-RIEMANNIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

Öz

Kaynakça

• Beem, J. K., Ehrlich, P. E. and Easley, K. L. Global Lorentzian geometry (Pure and Applied Mathematics 202, Marcel Dekker, Inc., New York, 1996).
• Duggal, K. L. and Bejancu, A. Lightlike Submanifolds of Semi - Riemannian Manifolds and Applications(Kluwer Acad. Publishers, Dordrecht, 1996).
• Gray, A. Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715–737, 1967.
• Falcitelli, M., Ianus, S. and Pastore, A. M. Riemannian Submersions and Related Topics (World Scientific, 2004).
• Kupeli, D. N. Singular Semi-Riemannian Geometry (Kluwer Dortrecht, 1996).
• Nomizu, K. Fundamentals of Linear Algebra (McGraw Hill, New York, 1966).
• O’Neill, B. The fundamental equations of a submersion, Michigan Math. J. 13, 459ˆu-469, 1966.
• O’Neill, B. Semi-Riemannian Geometry with Application to Relativity (Academic Press, New York, 1983).
• S¸ahin, B. On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds, Mediterranean J. Math. 5, 273–284, 2008.