
Torsion of the curve
a) Prove for each t for which http://s3.amazonaws.com/answerboard...8612507973.gifthere is a number τ (t) such that http://s3.amazonaws.com/answerboard...2050003341.gif. The number τ (t) is called the torsion of the curve at t.
(b) Show that http://s3.amazonaws.com/answerboard...5175003567.gif and that a positive value of τ corresponds to the curve twisting toward N.
(c) Verify the validity of the following Fre'netSerret formulas:
http://s3.amazonaws.com/answerboard...6112502122.gif
http://s3.amazonaws.com/answerboard...9862507483.gif
http://s3.amazonaws.com/answerboard...9550005540.gif
(d) Show that if the curvature is identically zero, then the curve is a straight line
(e) Show that if the torsion is identically zero, then the curve lies in a plane
(f) If the torsion is identically zero and the curvature is a nonzero constant, then show that the curve is a circle.
I already have part (a) answered need help with the others though