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Zbl 1121.53022
Duggal, K.L.; Sahin, B.
Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds. (English)
[J] Acta Math. Hung. 112, No. 1-2, 107-130 (2006). ISSN 0236-5294; ISSN 1588-2632/e

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.
[Andreas Cap (Wien)]

MSC 2000:: *53C15 Geometric structures on manifolds
53C40 Submanifolds (differential geometry)
53C50 Lorentz manifolds, manifolds with indefinite metrics

Keywords: degenerate metric; CR-submanifold; Kaehler manifold

Cited in: Zbl 1252.53029

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