  We study a general configuration of parallel branes having co-dimension >2
situated inside a compact d-dimensional bulk space within the framework of a
scalar and flux field coupled to gravity in D dimensions, such as arises in the
bosonic part of some D-dimensional supergravities. A general relation is
derived which relates the induced curvature of the observable noncompact n
dimensions to the asymptotic behaviour of the bulk fields near the brane
positions. For compactifications down to n = D-d dimensions we explicitly solve
the bulk field equations to obtain the near-brane asymptotics, and by so doing
relate the n-dimensional induced curvature to physical near-brane properties.
In the special case where the bulk geometry remains nonsingular (or only
conically singular) at the brane positions our analysis shows that the
resulting n dimensions must be flat. As an application of these results we
specialize to n=4 and D=6 and derive a new class of solutions to chiral 6D
supergravity for which the noncompact 4 dimensions have de Sitter or anti-de
Sitter geometry.
