View source for Normal section

''of a smooth surface $\Phi$ at a point $P$ in a direction $\ell$''

The section of $\Phi$ by the plane passing through the normal to the surface (cf. [[Normal space (to a surface)]]) at $P$ and through the direction $\ell$ in the [[tangent plane]] to $\Phi$ at $P$. 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.

====References====
<table>
<TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Klingenberg,   "A course in differential geometry" , Springer  (1978)  (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>

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