Article ID Journal Published Year Pages File Type
4630047 Applied Mathematics and Computation 2012 7 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
Authors
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