Many cusped hyperbolic 3-manifolds do not bound geometrically

In this note we show that there exist cusped hyperbolic 3-mani-folds that embed geodesically but cannot bound geometrically. Thus, being a geometric boundary is a non-trivial property for such manifolds. Our result complements the work by Long and Reid on geometric boundaries of compact hyperbolic 4-manifolds and by Kolpakov, Reid, and Slavich on embedding arithmetic hyperbolic manifolds.