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The natural lift curves and the geodesic sprays for the spherical indicatrices of the pair of evolute-involute curves. (English) Zbl 1038.53003

The authors consider a pair of evolute-involute curves \((a,a^*)\) in \(E^3\) and the natural lift curves of the spherical indicatrices of the involute curve \(a^*\). Then, by assuming that the above natural lift curves are integral curves of the geodesic spray on the tangent bundle of a unit sphere, they obtain some results about the volute curve \(a\).

MSC:

53A04 Curves in Euclidean and related spaces
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