The metric of a warped space-time with two extra dimensions is established by means of the Einstein equations in six dimensions and the compactification of two extra dimensions on a square. It is shown that at every among two fixed points our manifold reduces to the five-dimensional Randall - Sundrum space-time and the hierarchy problem could be solved. | Communications in Physics, Vol. 24, No. 1 (2014), pp. 1-8 THE BULK METRIC IN THE THEORY WITH TWO EXTRA DIMENSIONS TRAN HUU PHAT Vietnam Atomic Energy Institute, 59 Ly Thuong Kiet, Hanoi, Vietnam PHAN HONG LIEN Military Academy of Technology, 236 Hoang Quoc Viet, Hanoi, Vietnam HA VAN CHUNG Hanoi National University of Education, 136 Xuan thuy, Hanoi, Vietnam E-mail: tranhuuphat41@ Received 25 December 2013 Accepted for publication 22 February 2014 Abstract. The metric of a warped space-time with two extra dimensions is established by means of the Einstein equations in six dimensions and the compactification of two extra dimensions on a square. It is shown that at every among two fixed points our manifold reduces to the five-dimensional Randall - Sundrum space-time and the hierarchy problem could be solved. Keywords: six dimensions, 6D Riemann manifold, bulk metric, compactification. I. INTRODUCTION The first idea of extra dimensions, as it is well known, have been proposed by Kaluza Klein in the 1920s to unify electromagnetism and gravity [1]. The expansion of space-time dimensions beyond the four is one of most interesting fields of modern theoretical physics. Besides the extended models of Standard Model (SM), the extra dimensions have been considered as the ways to investigate both old and open problems of particle physics and Cosmology, in the new physics beyond the SM to unify gravity with gauge interactions. Extra dimensions provide the solutions of hierarchy problem in the 5D Randall-Sundrum space-time [2], or in more extra dimensions [3]; the explanation of dark matter [4,5], neutrino physics in the 6D Universal Extra Dimensions (UED) model [6-9] ; the expective proposal for GUT based on String Theories with 10D or 11D [10,12]. Extra dimensional theories can lead to really significant physical consequences. Starting from two following important observations 1) Solving the mass hierarchy problem by means of the wrap factor attaching to the four .
