We study the geometry of semi-invariant lightlike submanifolds of an indefinite Kaehler manifold M admitting a quarter-symmetric non-metric connection D. We establish conditions for a proper totally umbilical semi-invariant lightlike submanifold of M admitting D to be a totally geodesic semi-invariant lightlike submanifold. We further derive some characterization theorems for a semi-invariant lightlike submanifold of M admitting D to be a semi-invariant lightlike product manifold. Finally, we obtain some necessary and sufficient conditions for a semi-invariant lightlike submanifold of M admitting D to be a minimal lightlike submanifold.

The authors would like to express our sincere gratitude to the referees of our paper for their valuable suggestions.