We study a lightlike hypersurface M of an indefinite nearly trans-Sasakian manifold M̄ with an (ℓ, m)-type connection such that the structure vector field ζ of M̄ is tangent to M. In particular, we focus on such lightlike hypersurfaces M for which the structure tensor field F is either recurrent or Lie recurrent, or such that M itself is totally umbilical or screen totally umbilical.

Keywords: (ℓ,m)-type connection, recurrent, Lie recurrent, lightlike hypersurface, indefi,nite nearly trans-Sasakian manifold.