I Meaning of the sign of the geodesic curvature

1. Nov 11, 2016

Leo Mar

My question is : what is the meaning of the geodesic curvature sign for a coordinate patch? for a surface? Thank you.

2. Nov 11, 2016

lavinia

how do you define geodesic curvature?

3. Nov 13, 2016

Leo Mar

Hello Lavinia, the geodesic curvature of a unit speed curve ϒ is the component of ϒ'' in the direction of S=n×T.

4. Nov 14, 2016

lavinia

OK.

Since the surface is oriented the unit tangent to the curve determines an oriented orthogonal direction by 90 degree rotation. This direction may be opposite to the projection of the curve's curvature vector onto the tangent plane. If the projection points opposite to the oriented normal then the geodesic curvature is negative.

Last edited: Nov 14, 2016