Abstract
In the present paper we investigate the dynamics of the S3−component of a J−trajectory in R×S3. We obtain several geometric properties for the projection curve on S2(12) via the Hopf map and we generate some examples with Mathematica. We also prove that the curves in S3 are geodesics on the Hopf tubes over the projection curve on the 2−sphere if and only if they are Legendre curves.
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