Higher dimensional space-time models provide us an alternative interpretation
of nature, and give us different dynamical aspects than the traditional
four-dimensional space-time models. Motivated by such recent interests,
especially for future numerical research of higher-dimensional space-time, we
study the dimensional dependence of constraint propagation behavior. The N+1
Arnowitt-Deser-Misner evolution equation has matter terms which depend on N,
but the constraints and constraint propagation equations remain the same. This
indicates that there would be problems with accuracy and stability when we
directly apply the N+1 ADM formulation to numerical simulations as we have
experienced in four-dimensional cases. However, we also conclude that previous
efforts in re-formulating the Einstein equations can be applied if they are
based on constraint propagation analysis.Comment: 4 pages, to appear in Gen. Rel. Gra