Bertrand curves in 3-dimensional space forms

We define Bertrand curves in a 3-dimensional Riemannian manifold and prove that a Frenet curve αα with the curvature κκ and the torsion ττ in a 3-dimensional simply connected space form is a Bertrand curve if and only if it satisfies τ=0τ=0 or κ+aτ=bκ+aτ=b for constants a   and b≠0.