Gaussian curvature

The Gaussian curvature of a surface at a point $p$ is the product

K=\\kappa_{1}\\kappa_{2}

of the two principal curvatures of the surface at $p$ .

The arithmetic mean of the principal curvatures at a point $p$

H=\\frac{\\kappa_{1}+\\kappa_{2}}{2}

is called the mean curvature of the surface at $p$ .

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