Time-like extra dimension and cosmological constant in brane models

We discuss the general models with one time-like extra dimension and parallel 3-branes on the space-time M-4 x M-1. We also construct the general brane models or networks with n space-like and m time-like extra dimensions and with constant bulk cosmological constant on the space-time M-4 x (M-1)(n+m), and point out that there exist two kinds of models with zero bulk cosmological constant: for static solutions, we have to introduce time-like and space-like extra dimensions, and for non-static solutions, we can obtain the models with only space-like extra dimension(s). In addition, we give two simplest models explicitly, and comment on the 4-dimensional effective cosmological constant. (C) 2001 Published by Elsevier Science B.V.