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$p$.