A normal plane is any plane containing the normal vector of a surface at a particular point.
The normal plane also refers to the plane that is perpendicular to the tangent vector of a space curve; (this plane also contains the normal vector) see Frenet–Serret formulas.
Normal section
The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane[1][2][3]
The curvature of the normal section is called the normal curvature.
If the surface is bow or cylinder shaped the maximum and the minimum of these curvatures are the principal curvatures.
If the surface is saddle shaped the maxima of both sides are the principal curvatures.
The product of the principal curvatures is the Gaussian curvature of the surface. (negative for saddle shaped surfaces)
The mean of the principal curvatures is the mean curvature of the surface, if (and only if) the mean curvature is zero the surface is a minimal surface.
See also
Normal bundle
Normal curvature
Principal curvature
References
Ruane, Irving Adler, with diagrams by Ruth Adler ; introduction to the Dover edition by Peter (2012). A new look at geometry (Dover ed.). Mineola, N.Y.: Dover Publications. p. 273. ISBN 0486498514.
Irving Adler (2013-08-30). A New Look at Geometry. Books.google.com.br. p. 273. Retrieved 2016-04-01.
Alfred Gray (1997-12-29). Modern Differential Geometry of Curves and Surfaces with Mathematica, Second ... Books.google.com.br. p. 365. Retrieved 2016-04-01.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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