Definition:Principal Directions of Curvature of Surface

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This page is about the principal directions of curvature of a surface. For other uses, see principal.

Definition

Let $S$ be a surface in space.

The curvature of $S$ in general depends on direction.

Let $P$ be a point on $S$.

The principal directions of the curvature of $S$ at $P$ are:

the direction of the tangent of $S$ at $P$ in which the curvature is at a minimum
the direction of the tangent of $S$ at $P$ in which the curvature is at a maximum.



This article is complete as far as it goes, but it could do with expansion.
In particular: Plenty of stuff taken for granted here. Background material in $3$-d geometry needed.
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Also see

  • Results about curvature can be found here.


Sources

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