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Generalized Cauchy--Riemann lightlike submanifolds of Kaehler manifolds

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Summary

We introduce a class of submanifolds, namely, Generalized Cauchy--Riemann (GCR) lightlike submanifolds of indefinite Kaehler manifolds. We show that this new class is an umbrella of invariant (complex), screen real [8] and CR lightlike [6] submanifolds. We study the existence (or non-existence) of this new class in an indefinite space form. Then, we prove characterization theorems on the existence of totally umbilical, irrotational screen real, complex and CR minimal lightlike submanifolds. We also give one example each of a non totally geodesic proper minimal GCR and CR lightlike submanifolds.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4

    K. L. Duggal

  2. Department of Mathematics, Inonu University, 44280, Malatya, Turkey

    B. Sahin

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  1. K. L. Duggal
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  2. B. Sahin
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Duggal, K., Sahin, B. Generalized Cauchy--Riemann lightlike submanifolds of Kaehler manifolds. Acta Math Hung 112, 107–130 (2006). https://doi.org/10.1007/s10474-006-0068-y

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  • DOI: https://doi.org/10.1007/s10474-006-0068-y

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