Curves on surfaces: Geodesics 1 Review of the geodesic curvature of the curves in the surface

1 Review of the geodesic curvature of the curves in the surface We first review the geodesic curvature of the curves in the surface introduced in section 4.1. Let M be a surface and let α be a curve in the surface M, parametrized by its arc-length (.i.e. α ′ = 1). By the " trick of the unit-vector " , α ′′ is perpendicular to α ′ , so (4.2.1) α ′′ = κ n n + κ g n × α ′ .