Helices associated to helical curves, relatively normal-slant helices and isophote curves

Helices associated to helical curves, relatively normal-slant helices and isophote curves | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 18 August 2025 V1 Latest version Share on Helices associated to helical curves, relatively normal-slant helices and isophote curves Author : Mehmet Önder 0000-0002-9354-5530 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175553115.58528243/v1 84 views 47 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract This study introduces a new type of general helix, called the associated helix, which is linked to a special surface curve. The main idea is to determine the parametric form of an associated helix by using the Darboux frame and the surface curvatures of specific surface curves, such as a helical curve, a relatively normal-slant helix, or an isophote curve. For each surface curve, a system of differential equations is derived, and by solving this system, the parametric form of the associated helix is obtained. MSC: 53A04, 53A05. Supplementary Material File (1. (cbü)helices assoc. to helical, rns, ic.doc) Download 1.22 MB Information & Authors Information Version history V1 Version 1 18 August 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords associated helix helical curve isophote curve relatively normal-slant helix Authors Affiliations Mehmet Önder 0000-0002-9354-5530 [email protected] Manisa Celal Bayar Universitesi Fen Edebiyat Fakultesi View all articles by this author Metrics & Citations Metrics Article Usage 84 views 47 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Mehmet Önder. Helices associated to helical curves, relatively normal-slant helices and isophote curves. Authorea . 18 August 2025. DOI: https://doi.org/10.22541/au.175553115.58528243/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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