Ukr. Mat. Zh. - 2016. - 68, № 7. - pp. 963-971
We introduce slant lightlike submersions from an indefinite almost Hermitian manifold onto a lightlike manifold. We establish existence theorems for these submersions. We also investigate the necessary and sufficient conditions for the leaves of the distributions to be totally geodesic foliations in indefinite almost Hermitian manifolds.