Difference between revisions of "Normal space (to a surface)"
From Encyclopedia of Mathematics
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| − | ''at a point | + | {{TEX|done}} |
| + | ''at a point $P$'' | ||
| − | The orthogonal complement | + | The orthogonal complement $N_PF$ to the tangent space $T_PF$ (see [[Tangent plane|Tangent plane]]) of the surface $F^m$ in $V^n$ at $P$. The dimension of the normal space is $n-m$ (the codimension of $F$). Every one-dimensional subspace of it is called a [[Normal|normal]] to $F$ at $P$. If $F$ is a smooth hypersurface, then it has a unique normal at every of its points. |
Latest revision as of 17:17, 30 July 2014
at a point $P$
The orthogonal complement $N_PF$ to the tangent space $T_PF$ (see Tangent plane) of the surface $F^m$ in $V^n$ at $P$. The dimension of the normal space is $n-m$ (the codimension of $F$). Every one-dimensional subspace of it is called a normal to $F$ at $P$. If $F$ is a smooth hypersurface, then it has a unique normal at every of its points.
Comments
References
| [a1] | W. Klingenberg, "Riemannian geometry" , de Gruyter (1982) (Translated from German) |
| [a2] | B.-Y. Chen, "Geometry of submanifolds" , M. Dekker (1973) |
How to Cite This Entry:
Normal space (to a surface). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_space_(to_a_surface)&oldid=17490
Normal space (to a surface). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_space_(to_a_surface)&oldid=17490
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article