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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivative of surface normal || tangent unit vector

**Physics Forums | Science Articles, Homework Help, Discussion**