+4.31. Let a(s) be a unit speed curve with kt = 0. Prove there is a curve
B(s) (s not arc length on B) so that a and B are Bertrand curves if and
only if there are constants 2 #0 and u with 1/2 = K + ut.
T
itan Dhan aviat

It is proved

Step-by-step explanation:

A curve immersed in the three-dimensional sphere is said to be a Bertrand curve if there exists another curve and a one-to-one correspondence between and such that both curves have common principal normal geodesics at corresponding points.

See attachment for the step by step solution of the given problem.