Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds

Duggal K. L. , Sahin B.

ACTA MATHEMATICA HUNGARICA, cilt.112, ss.107-130, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 112
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1007/s10474-006-0068-y
  • Sayfa Sayıları: ss.107-130


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.