A Note on the Construction of Complex and Quaternionic Vector Fields on Spheres
arXiv:1605.09207
Abstract
A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard -sphere is shown to be twice the number of linearly independent quaternionic vector fields plus , where $ d = 1 \mbox{ or } 3$.
10 pages