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 $M^4 \times M^1$. We also construct the general brane models or networks with $n$ space-like and $m$ time-like extra dimensions and with constant cosmological constant on the space-time $M^4\times (M^1)^{n+m}$, and point out that there exist two kinds of models with zero cosmological constant. For static solutions, we have to introduce time-like and space-like extra dimensions to obtain the models with zero cosmological constant. For non-static solutions, we can obtain the models with only space-like extra dimension(s) and zero cosmological constant. We also give two simplest models explicitly