## Embedding arithmetic hyperbolic manifolds

Given an n-dimensional hyperbolic manifold M, it is reasonable to ask whether or not it can be realized as a totally geodesic, embedded submanifold of an (n+1)-dimensional hyperbolic manifold. If this is true, we say that M geodesically embeds. Determining whether or not a hyperbolic manifolds geodesically embeds is, in general, quite difficult.

However, if we restrict our attention to the case of arithmetic manifolds of simplest type, (a class of manifolds constructed using tools from number theory), we can show that, in many cases, they do indeed embed geodesically.