A New Representation of Canal Surfaces with Split Quaternions in Minkowski 3-Space

Kocakusakli E., Tuncer O. O., Gok I., Yayli Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.27, no.2, pp.1387-1409, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s00006-016-0723-5
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1387-1409
  • Keywords: Canal surface, Minkowski space, Spherical indicatrix of space curve, Split quaternion, Tubular surface, EUCLIDEAN-SPACE E-2(4), TUBULAR SURFACES, CURVES, ROTATIONS, HELICES
  • Hacettepe University Affiliated: No

Abstract

In this paper, we introduce canal surfaces determined by spherical indicatrices of any spatial curve in Minkowski 3-space by means of timelike split quaternions. Moreover, using orthogonal matrices corresponding to these quaternions, the canal surfaces are obtained as homotetic motions. Then, we investigate a relationship between the canal surfaces and unit split quaternions. Finally, we present some interesting examples with figures.