Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds. (English) Zbl 1265.53039
Summary: We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) light-like submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR light-like subcases [K. L. Duggal and B. Sahin, Int.J.Math.Math.Sci. 2007, Article ID 57585, 21 p. (2007; Zbl 1147.53044)] and real hypersurfaces [T. H. Kang et al., Indian J.Pure Appl.Math. 34, No. 9, 1369–1380 (2003; Zbl 1046.53053)]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-light-like submanifolds.
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C40 | Global submanifolds |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
