We extend a recently discovered, nonsingular 6-dimensional brane, solution to D = 4 + n dimensions. As with the previous 6D solution the present solution provides a gravitational trapping mechanism for fields of spin 0, 1 2 , 1, and 2. There is an important distinction between two extra dimensions and n extra dimensions that makes this more than a trivial extension. In contrast to gravity in n > 2 dimensions, gravity in n = 2 dimensions is conformally flat. The stress-energy tensor required by this solution has reasonable physically properties, and for n = 2 and n = 3 can be made to asymptotically go to zero as one moves away from the brane.
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