Unlike the 2-sphere, the 3-sphere admits nonvanishing vector fields (sections of its tangent bundle). One can even find three linearly independent and nonvanishing vector fields. These may be taken to be any left-invariant vector fields forming a basis for the Lie algebra of the 3-sphere. This implies that the 3-sphere is parallelizable. It follows that the tangent bundle of the 3-sphere is trivial. For a general discussion of the number of linear independent vector fields on a -sphere, see the article vector fields on spheres.
Unlike the 2-sphere the 3-sphere admits nonvanishing vector fields (sections of its tangent bundle) One can even find three linearly independent and nonvanishing vector fields These may be taken to be any left-invariant vector fields forming a basis for the Lie algebra of the 3-sphere This implies that the 3-sphere is parallelizable It follows that the tangent bundle of the 3-sphere is trivial For a general discussion of the number of linear independent vector fields on a -sphere see the article vector fields on spheres