D3+D6 solution and D4+D6 solution Original Research Article

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the ZN identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S3 part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.