Mean and Guassian curvatures

Several traditional measures of curvature are encoded in the differential of the Gauss map. Gaussian curvature is defined as the determinant of $ dN_p$ : $ K = k_1 k_2$ . The mean curvature is defined as the negative of half of the trace of $ dN_p$ : $ H = (k_1 + k_2) / 2$ .



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