On the deformation of linear r-fields

✍ Scribed by F.O. Farid

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 225 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.02.018

✦ Synopsis

We study the question: For which (r, n) can a linear r-field on the (n -1)-sphere in an n-dimensional real linear space be deformed through a continuous path of linear r-fields into an orthonormal r-field. We provide complete answers for the cases: (r, n) = (2, 4), (3, 4), and provide several partial results for the cases (r, n) = (2, 2m), where m is an even integer satisfying m 4. Characterizations of linear r-fields are pivotal in the investigation.