Principal Curvatures
The Maximum and Minimum of the Normal Curvature 
and 
at a given point on asurface are called the principal curvatures. The principal curvatures measure the Maximum and Minimumbending 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) |
 | |  | (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.
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