Hypersurface Family with a Common Isoasymptotic Curve

BAYRAM E., KASAP E.

Geometry, vol.2014, pp.1-6, 2014 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 2014
  • Publication Date: 2014
  • Doi Number: 10.1155/2014/623408
  • Journal Name: Geometry
  • Page Numbers: pp.1-6
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present paper, we handle the problem of finding a hypersurface family from a given asymptotic curve in R^4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. We illustrate this method by presenting some examples.