Jin, Dae Ho Transversal half lightlike submanifolds of an indefinite Sasakian manifold. (English) Zbl 1233.53006 J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 18, No. 1, 51-61 (2011). In previous works, the geometry of light-like submanifolds \(M\) of an indefinite Sasakian manifold \(\bar M\) was studied, for totally umbilical and screen conformal \(M\) or for a totally umbilical screen distribution \(S(TM)\).In the present paper, transversal half light-like submanifolds of an indefinite Sasakian manifold are studied.A submanifold \(M\) of codimension \(2\) is called a half light-like submanifold if the radical distribution \(\text{Rad}(TM)=TM\cap TM^\perp\) of \(M\) is a vector subbundle of rank \(1\) of both the tangent bundle \(TM\) and the normal bundle \(TM^\perp\). The complementary non-degenerate distributions \(S(TM)\) and \(S(TM^\perp)\) of \(\text{Rad}(TM)\) in \(TM\) and \(TM^\perp\) are called screen and co-screen distribution, respectively. A half light-like submanifold \(M\) of an indefinite Sasakian manifold \(\bar M\) is called transversal if the characteristic vector field \(\zeta\) of \(\bar M\) belongs to the transversal vector bundle \(\text{tr}(TM)\) of \(M\).It is proved that there are no screen conformal transversal half light-like submanifolds of an indefinite Sasakian manifold; further, there are no transversal half light-like submanifolds of an indefinite Sasakian manifold such that the screen distribution is totally umbilical; and finally there are no proper totally umbilical transversal half light-like submanifolds of an indefinite Sasakian manifold \(\bar M\). Reviewer: Zdeněk Dušek (Olomouc) Cited in 2 Documents MSC: 53B25 Local submanifolds 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics Keywords:indefinite Sasakian manifold; transversal half light-like submanifold PDFBibTeX XMLCite \textit{D. H. Jin}, J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 18, No. 1, 51--61 (2011; Zbl 1233.53006) Full Text: DOI