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## Main Question or Discussion Point

Is it possible to have a tangent vector field on the unit 2-sphere x^2+y^2+z^2 =1 in

3D which vanishes at exactly one point? By the Poincare-Hopf index theorem

the index of such vector field at the point where it vanishes must be 2. Is that possible? If yes, can one write an explicit formula for such vector field.

3D which vanishes at exactly one point? By the Poincare-Hopf index theorem

the index of such vector field at the point where it vanishes must be 2. Is that possible? If yes, can one write an explicit formula for such vector field.