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 mgreater-or-equal, slanted4. Characterizations of linear r-fields are pivotal in the investigation.
Keywords :
Linear r-fields , Path connectedness , Orthonormal linear r-fields , Pfaffian of a real skew-symmetric matrix , Continuous linear deformation
