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  1. Second Fundamental Form

    Linked via "catenoids"

    Mean Curvature\_ ($H$): Half the trace of the shape operator.
    $$H = \frac{\kappa1 + \kappa2}{2} = \frac{LN - FM + ML - NE}{2(EG - F^2)}$$
    A surface is mean-curvature-constant if $H$ is constant across the surface (e.g., spheres\ and catenoids\).
    Gaussian Curvature\_ ($K$): The determinant of the shape operator.