We analyze 3D reconstructed surfaces based on previously reported high frequency measurements of flame edge location across expanding flames using Mie scatter. For the first time, principal curvatures of flame surfaces are estimated from eigenvalues of the second fundamental forms of the reconstructed surfaces, allowing the determination of the statistics of mean and Gaussian curvatures as a function of time and thus flame mean radius. Measurements and analysis were made for both lean methane and hydrogen mixtures as a function of time and turbulence levels. The mean 3D flame curvature was found to be inversely proportional to flame radius, and relatively insensitive to turbulence intensity, even in the case of larger, more planar flames. Mean 3D curvatures across the flame brush were determined to be positive (convex) towards the reactant mixture at the leading edge, and negative (concave) towards the trailing edge, as predicted from DNS measurements. The mean and probability distributions of 3D mean curvatures were found to be significantly different than 2D curvatures extracted from the central planes, with the 3D measurements showing much narrower distributions and lower values. Differences between 3D and 2D measurements were different by an order of magnitude in the case of hydrogen flames, possibly owing to the onset of thermodiffusive instabilities which affect the local fine structure of the flame.