Differential Gemometry
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question 17, page 55 Shifrin's book
Below is the question : 17
How is the Frenet frame along an asymptotic curve related to the geometry of the surface?
Suppose K.P / < 0. If C is an asymptotic curve with .P / ¤ 0, prove that its torsion satisfies
p
j.P /j D
K.P /. (Hint: If we choose an orthonormal basis fU; Vg for T P .M / with U tangent
to C , what is the matrix for S P ? See the Remark on p. 47.)
Note : please check the file also in order to solve the question .
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