Gaussian Curvature

Abstract

In differential geometry, the Gaussian curvature or Gauss curvature of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point. It is an intrinsic measure of curvature, depending only on distances that are measured on the surface, not on the way it is isometrically embedded in any space. It is named after Carl Friedrich Gauss, and is the content of his Theorema egregium.Symbolically, the Gaussian curvature Κ is defined aswhere κ1 and κ2 are the principal curvatures.