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

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory