## Bertrand curves in 3-dimensional space forms.(English)Zbl 1287.53011

Summary: We define Bertrand curves in a 3-dimensional Riemannian manifold and prove that a Frenet curve $$\alpha$$ with curvature $$\kappa$$ and torsion $$\tau$$ in a 3-dimensional simply connected space form is a Bertrand curve if and only if it satisfies $$\tau =0$$ or $$\kappa +a\tau =b$$ for constants $$a$$ and $$b\neq 0$$.

### MSC:

 53B25 Local submanifolds 53A04 Curves in Euclidean and related spaces

### Keywords:

Bertrand curve; helix; general helix; space form
Full Text:

### References:

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