We present metric solutions in six and higher dimensions with a bulk cosmological constant, where gravity is localized on a 3-brane. The corrections to four-dimensional gravity from the bulk continuum modes are power-law suppressed. Furthermore, the introduction of a bulk "hedgehog" magnetic field leads to a regular geometry, and can localize gravity on the 3-brane with either positive, zero or negative bulk cosmological constant.
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This work was supported by the FNRS, contract no. 21-55560.98.