# Normal space (to a surface)

From Encyclopedia of Mathematics

*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=32594

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article