Let u_p be a unit tangent vector of a regular surface M subset R^3. Then the normal curvature of M in the direction u_p is κ(u_p) = S(u_p)·u_p, where S is the shape operator. Let M subset R^3 be a regular surface, p element M, x be an injective regular patch of M with p = x(u_0, v_0), and v_p = a x_u(u_0, v_0) + b x_v(u_0, v_0), where v_p element M_p.

curvature | fundamental forms | Gaussian curvature | mean curvature | principal curvatures | shape operator | tangent vector