2019
DOI: 10.22190/fumi1902261y
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Abstract: We dene a Bertrand-B curve in Riemannian manifold M such that thereexists an isometry \phi of M, that is, \left( \phi \circ \beta \right) (s)=X\left( s,t(s)\right) and the binormal vector of another curve \beta is the paralel vector of binormal vector of \alpha at corresponding points. We obtain the conditions of existence of a Bertrand-B curve in the event E^3, S^3 and H^3 of M. The rst of our main results is that the curve \alpha in E^3 is a Bertrand-B curve if and only if it is planar. Second one, we prove … Show more

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“…By following the steps similar to those of Bertrand, this topic was expanded to different moving frames. For example, the studies [21], [14] and [7] expanded this topic to the type-2 Bishop frame, Darboux frame and qframe, respectively. Also, many mathematicians presented various studies about the concept of Bertrand curve couple with different perspectives.…”
Section: Introductionmentioning
confidence: 99%
“…By following the steps similar to those of Bertrand, this topic was expanded to different moving frames. For example, the studies [21], [14] and [7] expanded this topic to the type-2 Bishop frame, Darboux frame and qframe, respectively. Also, many mathematicians presented various studies about the concept of Bertrand curve couple with different perspectives.…”
Section: Introductionmentioning
confidence: 99%