In
differential geometry, the
Gaussian curvature or
Gauss curvature Κ of a
surface at a point is the product of the
principal curvatures,
κ1 and
κ2, at the given point:
For example, a sphere of radius
r has Gaussian curvature
1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere. The Gaussian curvature can also be negative, as in the case of a
hyperboloid or the inside of a
torus.