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Classification of special triharmonic curves in 3D Sol space

Published on:

2 April 2024

Primary Category:

Differential Geometry

Paper Authors:

Stefano Montaldo,

Andrea Ratto

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Key Details

Completely classifies constant-torsion triharmonic curves in 3D Sol space

Proves only one proper triharmonic helix exists, with curvature and torsion 1/2

Shows this curve makes a constant angle with a Killing field

Derives equations for triharmonic Frenet curves in Sol space

Defines triharmonic curves and studies their properties

AI generated summary

Classification of special triharmonic curves in 3D Sol space

This paper classifies a special type of triharmonic curves, with constant geodesic curvature and torsion, in the 3-dimensional Sol space. It proves only one such curve exists, with curvature 1/2 and torsion ±1/2. This curve forms a constant angle with a Killing field of the Sol space.

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