The degenerate nature of the metric on null hypersurfaces creates many difficulties
when attempting to define a covariant derivative on null submanifolds. This dissertation
investigates these challenges and provides a technique for defining a connection on null
hypersurfaces in some cases. Recent approaches using decomposition to define a covariant
derivative on null hypersurfaces are investigated, with examples demonstrating the limitations
of the methods. Motivated by Geroch's work on asymptotically flat spacetimes,
conformal transformations are used to construct a covariant derivative on null hypersurfaces.
In addition, a condition on the Ricci tensor is given to determine when this
construction can be used. All of the results are motivated through a sequence of examples
of null surfaces on which the covariant derivative is defined. Finally, a covariant derivative
operator is given for the class of spherically symmetric hypersurfaces
