Open AccessON THE EXTREMAL CURVATURE AND TORSION OF STEREOGRAPHICALLY PROJECTED ANALYTIC CURVES
Author(s) -
Stephen M. Zemyan
Publication year - 1997
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.28.1997.4324
Subject(s) - mathematics , curvature , torsion (gastropod) , torsion of a curve , mathematical analysis , pure mathematics , geometry , center of curvature , scalar curvature , medicine , surgery
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.