Parametric Representation of a Hypersurface Family With a Common Spatial Geodesic
Differential Geometry
2016-01-20 v2
Abstract
In this paper, we study the problem of finding a hypersurface family from a given spatial geodesic curve in R4. We obtain the parametric representation for a hypersurface family whose members have the same curve as a given geodesic curve. Using the Frenet frame of the given geodesic curve, we present the hypersurface as a linear combination of this frame and analyse the necessary and sufficient condition for that curve to be geodesic. We illustrate this method by presenting some examples.
Keywords
Cite
@article{arxiv.1305.0411,
title = {Parametric Representation of a Hypersurface Family With a Common Spatial Geodesic},
author = {Ergin Bayram and Emin Kasap},
journal= {arXiv preprint arXiv:1305.0411},
year = {2016}
}
Comments
17 pages, 3 figures