Khoza, Jabulile2024-10-242024-10-242022Khoza, Jabulile. (2022). On the Geometry of Lightlike Hypersurfaces [Master’s dissertation, University of the Witwatersrand, Johannesburg]. WireDSpace.https://hdl.handle.net/10539/41922https://hdl.handle.net/10539/41922A dissertation submitted in fulfillment of a Masters degree at the University of the Witwatersrand, Johannesburg-South Africa, Johannesburg 2022The study of lightlike geometry in semi-Riemannian manifolds was introduced by A. Bejancu and K. L. Duggal in their book [3]. The book laid a foundation for the study of lightlike submanifolds by providing some constructions on such subspaces. In this research, we focus on the study of lightlike hypersurfaces of semi-Riemannian manifolds, i.e. submanifolds of codimension one. In this line, we prove necessary and sufficient conditions for a lightlike hypersurface of a semi-Riemannian space form to be totally umbilical, screen conformal and screen almost conformal (see Theorem 2.5.2, 2.5.4 and 2.5.5)en© 2022 University of the Witwatersrand, Johannesburg. All rights reserved. The copyright in this work vests in the University of the Witwatersrand, Johannesburg. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of University of the Witwatersrand, Johannesburg.Semi-RiemannianLightlike hypersurfacesUCTDSDG-3: Good health and well-beingDissertationUniversity of the Witwatersrand, Johannesburg