Normal space (to a surface)
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.
|[a1]||W. Klingenberg, "Riemannian geometry" , de Gruyter (1982) (Translated from German)|
|[a2]||B.-Y. Chen, "Geometry of submanifolds" , M. Dekker (1973)|
Normal space (to a surface). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_space_(to_a_surface)&oldid=32594