D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the Dg branes in the near core region of D6 brane. From the D = 11 solutions (M3 branes and M4 branes with the ZN identificat ions in the transverse space) we obtain the D = 10 supergravity solutions o f D3 branes localized within D6 branes and D4 branes localized within D6 br anes by reducing the dimension down to D = 10 along a circular direction of S-3 part of the transverse space. M3 brane solution leads to D = 10 backgr ound representing D3 branes localized on D6 branes in the region close to t he D6 branes core. M4 branes lead to the D4 branes localized on D6 branes i n the region close to the D6 brane core. (C) 2001 Published by Elsevier Sci ence B.V.