  Let X be a manifold equipped with a complete Riemannian metric of constant
negative curvature and finite volume. We demonstrate the finiteness of the
collection of totally geodesic immersed hypersurfaces in X that lie in the
zero-level set of some Laplace eigenfunction. For surfaces, we show that the
number can be bounded just in terms of the area of the surface. We also provide
constructions of geodesics in hyperbolic surfaces that lie in a nodal set but
that do not lie in the fixed point set of a reflection symmetry.
