At parabolic points, one of the principal curvatures is zero.

Local maximum images of principal curvature values are used to define regions.

There are two principal curvatures identified, a maximum, ', and a minimum, '.

The eigenvalues are the principal curvatures of the surface.

Gaussian curvature is the product of the two principal curvatures.

The transformation can be viewed as locally rotating the principal curvature directions.

Principal curvature is the maximum and minimum normal curvatures at a point on a surface.

The table below lists common geometric shapes and a qualitative analysis of their two principal curvatures.

The paper Submanifolds with constant principal curvatures and normal holonomy groups.

At flat umbilic points both principal curvatures are zero.

At elliptical points, both principal curvatures have the same sign, and the surface is locally convex.

To get the principal curvature, the Hessian matrix is calculated:

The lemma describes a property of the principal curvatures of surfaces.

Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures.

The principal curvatures are the invariants of the pair consisting of the second and first fundamental forms.

At hyperbolic points, the principal curvatures have opposite signs, and the surface will be locally saddle shaped.

The mean curvature at is then the average of the principal curvatures , hence the name:

Principal direction is the direction of the principal curvatures.

The next step in the algorithm is to perform a detailed fit to the nearby data for accurate location, scale, and ratio of principal curvatures.

The helicoid has principal curvatures .

Principal directions - In differential geometry, one of the directions of principal curvature.

The ratio of the principal curvatures at every point on the mylar balloon is exactly 2, making it an interesting case of a Weingarten surface.

At umbilic points, both principal curvatures are equal and every tangent vector can be considered a principal direction.

Mathematically, these two curvatures are called the principal curvatures, c1 and c2, and their meaning can be understood by the following thought experiment.

Analysis of the principal curvature is important, since a number of biological membranes possess shapes that are analogous to these common geometry staples.