• Home
• Register an Account
• New Title Information Alerts
• Contact Us
• Overview of the Wessex Institute of Technology

Adobe PDF Reader is required to view our papers:

Curves and surfaces in the three dimensional sphere placed in the space of quaternions

Author(s): Yoshihiko Tazawa Abstract: In this article we will show how to use Mathematica in dealing with curves and surfaces in the three dimensional unit sphere S^ embedded in the four dimensional Euclidian space E\ Since S* is the Lie group of unit quater- nions and at the same time it is a space of constant curvature, the analogy of the theory of curves in E^ holds. We calculate curvature and torsion of curves in S^ by Mathematica. The Gauss map v of a surface in E^ is decomposed into the two maps v+ and z/_. If the surface is contained in 5^, we can define another Gauss map z/g. We use Mathematica to visualize the shapes of the images of these Gauss maps. Finally, the meaning of these images becomes clear through the notion of the slant surface. 1 Curves The space E* is re... Pages: 8 Size: 455 kb Paper DOI: 10.2495/IMS970591

Download the Full Article Price: US$ 0.00 This article is part of the WIT OpenView scheme and you can download the full text Adobe PDF article for FREE by clicking the 'Openview' icon below. Send this page to a colleague. This paper can be found in the following book Innovation in Mathematics Buy Book from Witpress.com

---

Download the Full Article This article is part of the WIT OpenView scheme and you can download the full text Adobe PDF article for FREE by clicking the 'Openview' icon to the right.