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KYUNGPOOK Math. J. 2019; 59(4): 783-795

Published online December 23, 2019

Copyright © Kyungpook Mathematical Journal.

Some Results on Null Hypersurfaces in (LCS)-manifolds

Samuel Ssekajja

School of Mathematics, University of Witwatersrand, Private Bag 3, Wits 2050, South Africa
e-mail : samuel.ssekajja@wits.ac.za or ssekajja.samuel.buwaga@aims-senegal.org

Received: January 7, 2019; Revised: June 25, 2019; Accepted: October 21, 2019

Abstract

We prove that a Lorentzian concircular structure (LCS)-manifold does not admit any null hypersurface which is tangential or transversal to its characteristic vector field. Due to the above, we focus on its ascreen null hypersurfaces and show that such hypersurfaces admit a symmetric Ricci tensor. Furthermore, we prove that there are no totally geodesic ascreen null hypersurfaces of a conformally flat (LCS)-manifold.

Keywords: null hypersurfaces, Ascreen null hypersurfaces, Lorentzian concircular structure manifolds.