# Line of curvature

From Diffgeom

## Definition

### Symbol-free definition

A curve on a regular surface is termed a **line of curvature** if it satisfies the following conditions:

- At every point on the curve the tangent vector to the curve is a principal vector (i.e. is in one of the principal directions) to the surface.
- The derivative of the standard unit normal to the surface along the curve, is a scalar function times the unit tangent vector to the curve
- The geodesic torsion of the curve vanishes everywhere

## Facts

### Rodrigues' formula

`Further information: Rodrigues' formula`