SURFACE FAMILY WITH A COMMON ASYMPTOTIC CURVE IN MINKOWSKI 3-SPACE

Şaffak Atalay G., BAYRAM E., Kasap E.

JOURNAL OF SCIENCE AND ARTS, no.2, pp.357-370, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2018
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.357-370
  • Keywords: Minkowski 3-space, surface family, asymptotic curve, GALILEAN SPACE G(3), PARAMETRIC REPRESENTATION, PENCIL, CURVATURE, LINE
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also present some interesting examples to show the validity of this study.