This site is being phased out.

Gaussian curvature

From Mathematics Is A Science
Jump to navigationJump to search

The Gaussian curvature of a surface is the product of the principal curvatures at the given point, $\kappa_1$ and $\kappa_2$. (Compare those to curvature of a curve.) Symbolically, the Gaussian curvature is $$K = \kappa_1 \kappa_2.$$

The Gaussian curvature is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is embedded in space (Theorema egregium).

See also Gauss-Bonnet theorem.