Stephen M. Zemyan, "On some new properties of the spherical curvature of stereographically projected analytic curves", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 721818, 12 pages, 2003. https://doi.org/10.1155/S016117120320819X
On some new properties of the spherical curvature of stereographically projected analytic curves
We discover new information about the spherical curvature of stereographically projected analytic curves. To do so, we first state formulas for the spherical curvature and spherical torsion of the curves on which result after stereographically projecting the image curves of analytic, univalent functions belonging to the class . We then derive results concerning the location of the critical points of the spherical curvature, considered both as a function of one and two variables. Further analysis leads to a maximum principle for the spherical curvature functions.
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