Backreacted Kahler geometry of wrapped branes

For supersymmetric solutions of D3-(M2-) branes with AdS(3)(AdS(2)) factor, it is known that the internal space is expressible as U(1) fibration over Kahler 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 Kahler geometry, and present a class of solutions which satisfy the Killing spinor equation.