Curves in three dimensional Riemannian space forms (Q5919181)

The author studies some properties of Bertrand curves in the 3-dimensional Riemannian sphere and also in a 3-dimensional hyperbolic space. Using a natural moving frame, necessary and sufficient conditions are found for the existence of a Bertrand curve. Moreover, the author obtains some examples of such curves in a Riemannian space form or a pseudo Riemannian space form and a pseudo Riemannian degenerate space form.