A Bertrand curve is defined as a special curve which shares its principal normals with another special curve, called Bertrand mate or Bertrand partner curve.
is a Bertrand curve, where a, [xi] are constant numbers.
The spherical curve f is a circle if and only if the corresponding Bertrand curve is a circular helix.
The spherical curve T(v) is a circle if and only if the corresponding Bertrand curve [[integral].
s]) whose principal normal direction coincides with that of original curve, then [gamma] is said to be a Bertrand curve.
Let [gamma] be a Bertrand curve with a[kappa] + b[tau] = 1 and [bar.
Conversely, every Bertrand curve can be represented in this form.
at each pair of corresponding points coincide with the line joining corresponding points then [subset] is called a Bertrand curve and the curve [?
whenever it is well defined, then c is called a weakened Bertrand curve and denoted by W B curve.
Bertrand curves are characterized as special curves whose curvature and torsion are in linear relation.
Ravani and Ku transported the notion of Bertrand curves to the ruled surfaces and called them Bertrand offsets .
A generalization of the Bertrand curves as general inclined curves in En.