International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 26, Pages 1633-1644

On some new properties of the spherical curvature of stereographically projected analytic curves

Stephen M. Zemyan

Department of Mathematics, The Pennsylvania State University, Mont Alto 17237-9799, PA, USA

Received 2 August 2002

Copyright © 2003 Stephen M. Zemyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 S2 which result after stereographically projecting the image curves of analytic, univalent functions belonging to the class 𝒮. 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.