Normal section
From Encyclopedia of Mathematics
of a smooth surface at a point
in a direction
The section of by the plane passing through the normal to the surface (cf. Normal space (to a surface)) at
and through the direction
in the tangent plane to
at
. The task of studying the local structure of a surface can be reduced to the same task for the family of curves formed by the normal sections of the surface at a given point in various directions (see Curvature; Normal curvature). The method of studying the local structure by means of normal sections can be generalized to surfaces of arbitrary dimension and arbitrary codimension.
Comments
References
[a1] | W. Klingenberg, "A course in differential geometry" , Springer (1978) (Translated from German) |
[a2] | B.-Y. Chen, "Geometry of submanifolds" , M. Dekker (1973) |
How to Cite This Entry:
Normal section. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_section&oldid=40020
Normal section. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_section&oldid=40020
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article