Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4603486 | Linear Algebra and its Applications | 2008 | 17 Pages |
Abstract
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.
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