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Transversal lightlike submanifolds of indefinite Kähler manifolds. (Transversal lightlike submanifolds of indefinite Kaehler manifolds.) (English) Zbl 1174.53324
Summary: We introduce semi-transversal, transversal and radical transversal lightlike submanifolds of indefinite Kähler manifolds. We observe that such lightlike submanifolds are different from CR-lightlike, screen CR and generalized CR-lightlike submanifolds. We study the existence (or non-existence) of such lightlike submanifolds in an indefinite space form. Then, we prove characterization theorems on the existence of semi-transversal lightlike submanifolds. We also give examples for semi-transversal, transversal, radical transversal, totally umbilical semi-transversal and minimal semi-transversal lightlike submanifolds of indefinite Kähler manifolds.

MSC:
53C40Global submanifolds (differential geometry)
53C42Immersions (differential geometry)
53C50Lorentz manifolds, manifolds with indefinite metrics