Show the gradient field on a surface

Plot3D[(x ^ 2 + y ^ 2) Exp[1 - x ^ 2 - y ^ 2], {x, -3, 3}, {y, -3, 3}, PlotStyle -> Texture[StreamPlot[Evaluate[-D[(x ^ 2 + y ^ 2) Exp[1 - x ^ 2 - y ^ 2], {{x, y}}]], {x, -3, 3}, {y, -3, 3}, Frame -> None, ImageSize -> Large]], Mesh -> None, ImageSize -> Large, PlotPoints -> 35]

-Graphics3D-