Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. (English) Zbl 1121.53022

Duggal, K. L.; Sahin, B.

Acta Math. Hung. 112, No. 1-2, 107-130 (2006).

This paper introduces and studies a class of lightlike submanifolds in indefinite Kähler manifolds. This class, called generalized Cauchy–Riemann (GCR) submanifolds, contains Cauchy–Riemann and so called Screen Cauchy–Riemann submanifolds. In an introductory section, the authors recall some facts on lightlike submanifolds in pseudo–Riemannian manifolds. Next, they introduce the class of GCR–lightlike submanifolds in indefinite Kähler manifolds and study its relation to other classes of lightlike submanifolds. They prove some results on GCR–lightlike submanifolds which in addition are totally umbilical or minimal.

Reviewer: Andreas Cap (Wien)

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

Keywords:

degenerate metric; CR-submanifold; Kaehler manifold