Definition:Principal Curvatures of Surface

Definition

Let $S$ be a surface in space.

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

The principal curvatures of $S$ at $P$ are the curvatures at the principal directions of curvature of $S$ at $P$.

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. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Results about curvature can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): curvature
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): curvature