The statistical properties of dynamically triangulated manifolds (DT mfds) in
terms of the geodesic distance have been studied numerically. The string
susceptibility exponents for the boundary surfaces in three-dimensional DT mfds
were measured numerically. For spherical boundary surfaces, we obtained a
result consistent with the case of a two-dimensional spherical DT surface
described by the matrix model. This gives a correct method to reconstruct
two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a
scaling property of the volume distribution of minimum neck baby universes was
investigated numerically in the case of three and four dimensions, and we
obtain a common scaling structure near to the critical points belonging to the
strong coupling phase in both dimensions. We have evidence for the existence of
a common fractal structure in three- and four-dimensional simplicial quantum
gravity.Comment: 10 pages, latex, 6 ps figures, uses cite.sty and psfig.st
