Focal Representation of k-slant Helices in E^{m+1}
Differential Geometry
2013-05-13 v1
Abstract
A focal representation of a generic regular curve {\gamma} in E^{m+1} consists of the centers of the osculating hyperplanes. A k-slant helix {\gamma} in E^{m+1} is a (generic) regular curve whose unit normal vector V_{k} makes a constant angle with a fixed direction U in E^{m+1}. In the present paper we proved that if {\gamma} is a k-slant helix in E^{m+1}, then the focal representation C_{{\gamma}} of {\gamma} in E^{m+1} is a (m-k+2)-slant helix in E^{m+1}.
Keywords
Cite
@article{arxiv.1305.2337,
title = {Focal Representation of k-slant Helices in E^{m+1}},
author = {Gunay Ozturk and Betul Bulca and Bengu Bayram and Kadri Arslan},
journal= {arXiv preprint arXiv:1305.2337},
year = {2013}
}
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9 pages