Normal Curvature
Let 
be a unit Tangent Vector of a Regular Surface 
. Then the normalcurvature of 
in the direction is
 | (1) |
is the Shape Operator. Let be a Regular Surface, 
,
be an injective Regular Patch of with 
, and | (2) |
. Then the normal curvature in the direction 
is | (3) |
, 
, and 
are the coefficients of the first Fundamental Form and 
, 
, and 
are the coefficients of the second Fundamental Form.The Maximum and Minimum values of the normal curvature at a point on a Regular Surface are calledthe Principal Curvatures 
and 
.
References
Euler, L. ``Recherches sur la courbure des surfaces.'' Mém. de l'Acad. des Sciences, Berlin 16, 119-143, 1760. Gray, A. ``Normal Curvature.'' §14.2 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 270-273 and 277, 1993. Meusnier, J. B. ``Mémoire sur la courbure des surfaces.'' Mém. des savans étrangers 10 (lu 1776), 477-510, 1785.
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