Abstract
In this paper we study the functional of total bending B of unit vector fields on the standard sphere S 3. We prove that the Hopf vector fields on S 3 are critical points of B and that the Hesse form of B is positive semidefinite at the Hopf vector fields. They are also the vector fields of minimal total bending within a certain 5-dimensional manifold L 0 in the space of all unit vector fields. In order to prove this result we also give a classification of harmonic homogeneous quadratic polynomial maps from S 3 into S 2.
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