Classification of 5-dimensional space-time with parallel 3-branes

If the fifth dimension is a one-dimensional connected manifold, up to diffe omorphism, the only possible space-times will be M-4 x R-1, M-4 x R-1/Z(2), M-4 x S-1 and M-4 x S-1/Z(2). And there exist two possibilities for the co smological constant along the fifth dimension: the cosmological constant is constant, and the cosmological constant is sectionally constant. We constr uct general models with parallel 3-branes and constant/sectionally constant cosmological constant along the fifth dimension on those kinds of the spac e-times. Moreover, we point out that fur a compact fifth dimension, the sum of the brane tensions is zero, and for a non-compact fifth dimension, the sum of the brane tensions is positive. Furthermore, we assume the observabl e brane which includes our world should have positive tension, and obtain t hat the gauge hierarchy problem can be solved in those scenarios. We also d iscuss some simple models. (C) 2000 Elsevier Science B.V. All rights reserv ed.