Abstract

Let X be a continuous vector field on the unit Euclidean sphere S n − 1 ⊂ ℝ n centered at the origin. It is proved that X(−a) : −X(a) holds true for each vector a, then there is an orthonormal basis such that for any two vectors a and b in the basis one has X(a) ⋅ b + a ⋅ X(b) = 0. Bibliography: 1 title.

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