## Principal Curvatures

The Maximum and Minimum of the Normal Curvature and at a given point on a surface are called the principal curvatures. The principal curvatures measure the Maximum and Minimum bending of a Regular Surface at each point. The Gaussian Curvature and Mean Curvature are related to and by

 (1) (2)

This can be written as a Quadratic Equation
 (3)

which has solutions
 (4) (5)

See also Gaussian Curvature, Mean Curvature, Normal Curvature, Normal Section, Principal Direction, Principal Radius of Curvature, Rodrigues's Curvature Formula

References

Geometry Center. Principal Curvatures.'' http://www.geom.umn.edu/zoo/diffgeom/surfspace/concepts/curvatures/prin-curv.html.

Gray, A. Normal Curvature.'' §14.2 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 270-273, 277, and 283, 1993.