There's a problem I'm stucked on it. I wonder if anybody is able to help me because I tried almost every idea that I could thougth of. Here it is:
If $ u $ is a fixed direction and for any point $ s $ of a space curve
$ \left< B(s) , u \right> = \mathrm{constant} $
holds then prove that there's a constant vector $ v $ such that for every point $ s $ we have $ \left< T,v \right> = \mathrm{constant} $
I wish somebody could help me.
[ $ B $ is the binormal vector of curve. ] [ the curve is prameterized with arc length ]