<abstract xmlns="http://www.w3.org/1999/xhtml"> The focal representation of a generic regular curve γ in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix γ in Em+1 is a (generic) regular curve whose unit normal vector Vk makes a constant angle with a fixed direction <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/Untitled-1.jpg"></inline-graphic></alternatives></inline-formula> in Em+1. In the present paper we proved that if γ is a k-slant helix in Em+1, then the focal representation Cγ of γ in Em+1 is an (m− k + 2)-slant helix in Em+1.</abstract>

The focal representation of a generic regular curve γ in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix γ in Em+1 is a (generic) regular curve whose unit normal vector Vk makes a constant angle with a fixed direction  in Em+1. In the present paper we proved that if γ is a k-slant helix in Em+1, then the focal representation Cγ of γ in Em+1 is an (m− k + 2)-slant helix in Em+1.

Focal representation of k-slant Helices in Em+1

Department of Mathematics Kocaeli University, Turkey

Department of Mathematics Uludağ University, Turkey

Department of Mathematics Balıkesir University, Turkey

Acta Universitatis Sapientiae, Mathematica

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Focal representation of k-slant Helices in E

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The focal representation of a generic regular curve γ in Em+1 consists of the centers of the osculating hyperplanes. A k-slant helix γ in Em+1 is a (generic)...

Focal representation of k-slant Helices in E^m+1

Published Online: Feb 09, 2016

Page range: 200 - 209

Received: Oct 22, 2014

DOI: https://doi.org/10.1515/ausm-2015-0013

Keywords
Frenet curve, focal curve, slant helix

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Focal representation of k-slant Helices in Em+1

Published Online: Feb 09, 2016

Page range: 200 - 209

Received: Oct 22, 2014

DOI: https://doi.org/10.1515/ausm-2015-0013

KeywordsFrenet curve, focal curve, slant helix

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Focal representation of k-slant Helices in E^m+1

Keywords
Frenet curve, focal curve, slant helix