## You are here

Homeline of curvature

## Primary tabs

# line of curvature

A line $\gamma$ on a surface $S$ is a line of curvature of $S$, if in every point of $\gamma$ one of the principal sections has common tangent with $\gamma$.

By the parent entry, a surface $F(x,\,y,\,z)=0$, where $F$ has continuous first and second order partial derivatives, has two distinct families of lines of curvature, which families are orthogonal to each other.

For example, the meridian curves and the circles of latitude are the two families of the lines of curvature on a surface of revolution.

On a developable surface, the other family of its curvature lines consists of the generatrices of the surface.

A necessary and sufficient condition for that the surface normals of a surface $S$ set along a curve $c$ on $S$ would form a developable surface, is that $c$ is a line of curvature of $S$.

## Mathematics Subject Classification

53A05*no label found*26B05

*no label found*26A24

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections