Backreacted Kähler geometry of wrapped branes

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 Kähler 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 Kähler geometry, and present a class of solutions which satisfy the Killing spinor equation.