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 $p$.

Title	Gaussian curvature
Canonical name	GaussianCurvature
Date of creation	2013-03-22 17:00:56
Last modified on	2013-03-22 17:00:56
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	6
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 53A05
Synonym	total curvature
Synonym	total normal curvature
Related topic	MeanCurvatureAtSurfacePoint
Defines	mean curvature