Some remarks on invariant lightlike submanifolds of indefinite Sasakian manifold - Samuel Ssekajja (Arab Journal of Mathematical Sciences, 2022)
Purpose – The author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1. Design/methodology/approach – The author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7. Findings – The author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4). Originality/value – To the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.