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Loxodromes on hypersurfaces of revolution

Jacob Blackwood, Adam Dukehart and Mohammad Javaheri

Vol. 10 (2017), No. 3, 465–472
Abstract

A loxodrome is a curve that makes a constant angle with the meridians. We use conformal maps and the notion of parallel transport in differential geometry to investigate loxodromes on hypersurfaces of revolution and their spiral behavior near a pole.

Keywords
loxodromes, surfaces of revolution
Mathematical Subject Classification 2010
Primary: 53A04, 53A05, 53A07, 14H50, 14Q10
Milestones
Received: 17 November 2015
Revised: 17 November 2015
Accepted: 2 May 2016
Published: 14 December 2016

Communicated by Gaven Martin
Authors
Jacob Blackwood
School of Science
Siena College
515 Loudon Road
Loudonville, NY 12211
United States
Adam Dukehart
School of Science
Siena College
515 Loudon Road
Loudonville, NY 12211
United States
Mohammad Javaheri
School of Science
Siena College
515 Loudon Road
Loudonville, NY 12211
United States