ON THE EXTREMAL CURVATURE AND TORSION OF STEREOGRAPHICALLY PROJECTED ANALYTIC CURVES
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Abstract
In this paper, we first derive formulas for the curvature and torsion of curves on $S^2$ produced by stereographically projecting the image curves of analytic, univalent functions belonging to the class $\mathcal S$. We are concerned here with the problems of determining the extreme values of the curvatures and torsions, as well as the functions belonging to $\mathcal S$ which attain these extreme values. An analysis of the asymptotic behavior of these curvature and torsion formulas will allow for the formulation of plausible conjectures.
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References
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