International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 721818 | https://doi.org/10.1155/S016117120320819X

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

Received02 Aug 2002

Abstract

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.

Copyright © 2003 Hindawi Publishing Corporation. 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.


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