Definition:Principal Directions of Curvature of Surface

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.

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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