No continuous nonvanishing tangent vector field can exist on an even-dimensional sphere S^(2n). Follows from Poincaré-Hopf: the sum of indices of zeros of any vector field equals the Euler characteristic, and χ(S^(2n)) = 2. …
No continuous nonvanishing tangent vector field can exist on an even-dimensional sphere S^(2n). Follows from Poincaré-Hopf: the sum of indices of zeros of any vector field equals the Euler characteristic, and χ(S^(2n)) = 2. …