View source for Normal space (to a surface)

{{TEX|done}}
''at a point $P$''

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.



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Klingenberg,   "Riemannian geometry" , de Gruyter  (1982)  (Translated from German)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  B.-Y. Chen,   "Geometry of submanifolds" , M. Dekker  (1973)</TD></TR></table>