Let be w=w(σ) a curve on a surface parametrized by the arc length (the natural parametrization). Consider the m surface normal along this curve as the function of the σ arc length of the curve. Prove that m'(σ) is parallel to the t(σ) tangent unit vector of the curve for all σ, IFF this curve is a curvature line.(adsbygoogle = window.adsbygoogle || []).push({});

I would appreciate if you could help me!

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# Derivative of surface normal || tangent unit vector

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