Quaternionic Shape Operator

Aslan S., YAYLI Y.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.27, no.4, pp.2921-2931, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.1007/s00006-017-0804-0
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2921-2931
  • Keywords: Surfaces, Shape operator, Darboux frame, Quaternions, Rotation matrices, Homothetic motions, CANAL SURFACES
  • Ankara University Affiliated: Yes

Abstract

The shape operator is one of the most important research tools in differential geometry of surfaces. It uses the tangent vectors on the surface, extensively the tangent vectors of the parameter curves on the surface, and the normal vectors of the surfaces. Quaternions have the practical method in the rotation in the Euclidean 3-space. The main goal of our paper is to use quaternions in the research of the surfaces. Firstly, we have given the shape operator with Darboux frame along the curve in the surface. Then, the quaternionic shape operator is defined by the quaternion. Also, we have obtained some results related to the quaternionic shape operator and its matrix representation.