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

Stephen M. Zemyan

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1633-1644
Number of pages12
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2003
Issue number26
DOIs
StatePublished - Dec 1 2003

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Curvature
Curve
Univalent Functions
Maximum Principle
Torsion
Critical point

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

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On some new properties of the spherical curvature of stereographically projected analytic curves. / Zemyan, Stephen M.

In: International Journal of Mathematics and Mathematical Sciences, Vol. 2003, No. 26, 01.12.2003, p. 1633-1644.

Research output: Contribution to journalArticle

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