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 GaussianCurvature 2013-03-22 17:00:56 2013-03-22 17:00:56 Mathprof (13753) Mathprof (13753) 6 Mathprof (13753) Definition msc 53A05 total curvature total normal curvature MeanCurvatureAtSurfacePoint mean curvature