  For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is
known that the internal space is expressible as U(1) fibration over K\"ahler
space which satisfies a specific partial differential equation involving the
Ricci tensor. In this paper we study the wrapped brane solutions of D3 and
M2-branes which were originally constructed using gauged supergravity and
uplifted to D=10 and D=11. We rewrite the solutions in canonical form, identify
the backreacted K\"ahler geometry, and present a class of solutions which
satisfy the Killing spinor equation.
