  In this paper, we deal with the conjecture of 'Quantum Unique Ergodicity'. Z.
Rudnick and P. Sarnak showed that there is no 'strong scarring' on closed
geodesics for arithmetic congruence surfaces derived from a quaternion division
algebra. We extend this result to a class of three-dimensional Riemannian
manifolds X=Gamma\H^3 that are again derived from quaternion division algebras.
We show that there is no 'strong scarring' on closed geodesics or on
Gamma-closed imbedded totally geodesics surfaces of X.
