<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

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

Focal representation of k-slant Helices in E

{"article-title":{"content":"Focal representation of k-slant Helices in E","sup":"m+1"}}

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

Data publikacji: 09 lut 2016

Zakres stron: 200 - 209

Otrzymano: 22 paź 2014

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

Słowa kluczowe
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

Data publikacji: 09 lut 2016

Zakres stron: 200 - 209

Otrzymano: 22 paź 2014

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

Słowa kluczoweFrenet 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

Słowa kluczowe
Frenet curve, focal curve, slant helix