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Let be

I would appreciate if you could help me!

__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.I would appreciate if you could help me!

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