Page "Geodesic curvature" Paragraph 1

Consider a curve lying on a submanifold in ambient manifold, parametrized by arclength, with unit tangent vector.

The geodesic curvature is the norm of the projection of the derivative on the tangent plane to the submanifold.

Conversely the normal curvature is the norm of the projection of on the normal bundle to the submanifold at the point considered.