The rulings are

principal curvature lines with vanishing normal curvature and the Gaussian curvature vanishes at all surface points.

Thus the Gauss-Kronecker curvature G(p) is nothing but the product of the

principal curvature at p.

of the sampling) is given by the maximal

principal curvature.

In their framework, ridge and valley vertices are detected as zero-crossings, and then connected along the direction of

principal curvature.

The eigenvalues and eigenvectors of the quadratic form correspond to the

principal curvature values and to the directions of

principal curvature.

jik] = 0, in terms of the

principal curvature functions and three vector valued functions of one variable.

E] denote a

principal curvature with the induced hyperbolic and Euclidean metric on S respectively, then [kappa] and [[kappa].

Thus, the

principal curvatures can be obtained as the roots of the quadratic equation [k.

Different normal sections correspond to different curvatures at the evaluated point, and the maximum and minimum values of these curvatures are called the

principal curvatures [k.

Comparison of curves 2 and 3 with the results of [10] shows, that the rigidity of shallow spherical shells with the inclusion, for equal values of the dimensionless

principal curvatures and other parameters, significantly higher than the rigidity of corresponding cylindrical shells with inclusion.

In recent years, one of the principal research subjects already current in this theory is to characterize complete spacelike hypersurfaces with constant mean curvature (or constant scalar curvature) and two distinct

principal curvatures one of which is simple.

Finally, Chapter 7 is dedicated to various aspects of extrinsic geometry, such as Frenet formulas for curves, ruled and developable surfaces, the shape operator,

principal curvatures and curvature lines, etc.