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Classifying Geodesics on Cones: A New Approach

Published on:

24 March 2021

Primary Category:

Differential Geometry

Paper Authors:

Héctor Efrén Guerrero Mora

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Key Details

Presents new approach to classify geodesics on cones using rectifying curves

Proves a curve on any cone is a geodesic iff it is a rectifying curve

For circular cones, geodesics are rectifying curves and slant helices

Derives parametric equations for geodesics satisfying these properties

AI generated summary

Classifying Geodesics on Cones: A New Approach

This paper presents a novel method for classifying geodesic curves on cones in 3D Euclidean space. The key results establish necessary and sufficient conditions for a space curve to be a rectifying curve or to have its trace contained in a sphere. Using these conditions, the authors prove that a curve on a cone is a geodesic if and only if it is a rectifying curve, providing an alternate proof to prior work. For circular cones, geodesics are characterized as curves that are simultaneously rectifying and slant helices. The paper derives parametric equations for geodesics satisfying these properties. Overall, this provides new geometric insight into characterizing geodesics on conical surfaces.

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