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# 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
$p$.

Defines:

mean curvature

Related:

MeanCurvatureAtSurfacePoint

Synonym:

total curvature, total normal curvature

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

53A05*no label found*

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